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MODELING SPATIAL USE PATTERNS OF WHITE-TAILED DEER 
IN THE FLORIDA EVERGLADES 



By 

CHRISTINE STEIBLE HARTLESS 



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A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL 

OF THE UNIVERSITY OF FLORIDA IN PARTL^L FULFILLMENT 

OF THE REQUIREMENTS FOR THE DEGREE OF 

DOCTOR OF PHILOSOPHY 

UNIVERSITY OF FLORIDA 

2000 



Copyright 2000 

by 

Christine Steible Hartless 



k.1 ,|iii«ii«q^.ivf •! ^^vmn^'^^^ 



To Glen~my husband, my soulmate, my lifemate- 

for his ability to help me see the 'big picture' 

and his unending encouragement and love. 



ACKNOWLEDGMENTS 

Funding was provided by the National Park Service (Cooperative Agreement No. 
CA-528039013) and by the Agricultural Women's Club Scholarship and the William & 
Elyse Jennings Scholarship. 

I would like to thank Drs. Ronald F. Labisky and Kenneth M. Portier, my 
committee cochairs, for their support, guidance, and patience as I delved deeper into 
building the simulation model. Thanks also go to the other members of my committee, 
Drs. Michael P. Moulton and George W. Tanner, and especially to Dr. Jon C. Allen for 
his generous donation of countless hours of computer time running simulations in his lab. 

I am immensely grateful to Margaret Boulay, Kristi MacDonald, Karl Miller, 
Robert Sargent, and Jodie Zultowsky-the graduate students who came before me and 
conducted the field research that is the foundation of the work in this dissertation. My 
thanks also go to the staff of Everglades National Park and Big Cypress National Preserve 
who were involved in the field research. Patty Cramer and Brad Stith helped me through 
the initial shock of C++ and programming IBSE simulations. 

My parents, Dan and Barbara Steible, are owed my deepest gratitude for their 
constant support and encouragement. I also wish to thank Emily Clark for reminding me 
that there is life outside graduate school and Mike Steible for helping me nurse my ailing 
car through the last several years. 

iv 



TABLE OF CONTENTS 

page 

ACKNOWLEDGMENTS iv 

ABSTRACT vii 

1 INTRODUCTION 1 

1.1. Simulation Models as Research Tools 3 

1 .2. Objectives 6 

1 .3. Dissertation Structure 7 

2 EVERGLADES ECOSYSTEM AND THE STUDY AREA 8 

2.1. The Everglades Ecosystem 8 

2.2. Study Area 10 

3 WHITE-TAILED DEER MODEL CALIBRATION DATA 24 

3.1. Data Collection Methods 24 

3.2. Data Summary Methods 25 

3.3. Data Simimary 30 

3.4. Discussion 36 

4 DEVELOPMENT, CALIBRATION, AND EVALUATION OF THE 
SIMULATION MODEL 39 

4.1. Approach and Technique 39 

4.2. Initial Model Parameterization 53 

4.3. Model Calibration Experiments 63 

4.4. Final Movement Model 82 

4.5. Evaluation Approach for the Final Movement Model 90 

4.6. Evaluation of the Final Movement Model for Females 91 

4.7. Evaluation of the Final Movement Model for Males 104 



5 WHITE-TAILED DEER MODEL VALIDATION DATA 117 

5.1. Data Collection and Summary Methods 117 

5.2. Data Summary 119 

5.3. Discussion 126 

6 VALIDATION OF THE SIMULATION MODEL UNDER 

FLOOD CONDITIONS 128 

6.1. Approach to Model Validation 128 

6.2. Model Validation Results 131 

6.3. Discussion 148 

7 CONCLUSIONS AND FUTURE RESEARCH DIRECTIONS 157 

7.1. Applications of the White-tailed Deer Movement Simulation Model 158 

7.2. Contributions to the Field of Ecological Modeling 159 

APPENDICES 

A CALIBRATION DATA SET 162 

B DESCRIPTION OF PARAMETER SYMBOLS USED IN THE 

CALIBRATION EXPERIMENTS 175 

C SUMMARY OF CALIBRATION EXPERIMENTS FOR FEMALES 177 

D SUMMARY OF CALIBRATION EXPERIMENTS FOR MALES 195 

E VALIDATION DATA SET 204 

LITERATURE CITED ! .'. . ! 212 

BIOGRAPHICAL SKETCH 223 



VI 



Abstract of Dissertation Presented to the Graduate School 

of the University of Florida in Partial Fulfillment of the 

Requirements for the Degree of Doctor of Philosophy 

MODELING SPATIAL USE PATTERNS OF WHITE-TAILED DEER 
IN THE FLORIDA EVERGLADES 

By 

Christine Steible Hartless 

August 2000 

Chair: Dr. Ronald F. Labisky 

Cochair: Dr. Kenneth M. Portier 

Major Department: Wildlife Ecology and Conservation 

As reliance on ecological simulation models increases, proper tools to facilitate 
their calibration and to increase their reliability become more important. Computer 
simulations enable scientists to model the effects of environmental catastrophes or 
management strategies on target populations without conducting expensive or difficult 
field experiments. 

Fractional factorial experiments and response surface methods are presented as 
design and analysis tools to optimize a simulation model with respect to competing 
algorithms and parameter values. Issues involving simulation "bum-in" time, the number 
of iterations required for a simulation to reach a steady-state, and its estimation are 
discussed. Use of discrepancy functions as quantitative measures of model fit and 
parameter estimation are examined. Predictive p-values are presented as a tool for 

vii 



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evaluation of the performance of a simulation model, relative to observed field data. 
Finally, these tools are integrated into an iterative approach for development of 
simulation models. 

An individual-based, spatially explicit (IBSE) simulation model of adult white- 
tailed deer {Odocoileus virginianus seminolus) movement patterns in the wet 
prairie/hardwood tree island habitat of the Florida Everglades illustrates the use of these 
techniques. Radio-telemetry data obtained from white-tailed deer on the boundary 
between Big Cypress National Preserve and Everglades National Park during three 
normal-to-dry years (1989-92) were used to develop and calibrate the IBSE simulation 
model. Radio-location data from this same population of deer collected just prior to and 
during a severe flood (1993-95) were used to validate this simulation. The simulation 
model can help predict impacts of changes in water management strategies and the 
impacts of floods and hurricanes on white-tailed deer in the Florida Everglades. 



vin 



CHAPTER 1 
INTRODUCTION 



The Florida Everglades is home to a diverse mixture of temperate and sub-tropical 
flora and a broad collection of fauna, including the Florida panther {Puma concolor 
coryi), the American alligator {Alligator mississipiensis), many species of wading birds, 
and the white-tailed deer {Odocoileus virginianus seminolus). The Everglades serves as 
an example of how anthropogenic activities can drastically change the appearance and 
function of an ecosystem. National attention was focused on the Everglades when 
Douglas (1947) described its natural and cultural history in her book, The Everglades: 
River of Grass, and when the Everglades National Park was established that same year. 
Since then, many scientists have focused their research on understanding the effects of the 
human-induced changes on this ecosystem and on finding ways to slow or reverse 
degradation of this unique ecosystem. 

White-tailed deer are an ecologically, culturally, and economically valuable 
wildlife resource throughout the United States (Langenau et al. 1984). White-tailed deer 
play an important role in the Everglades ecosystem, serving as the major prey of the 
endangered Florida panther (Maehr et al. 1990) and the bobcat {Lynx rufus) (Maehr and 
Brady 1986). These deer are non-migratory (Loveless 1959b) and exhibit extreme site 
fidelity, even under adverse environmental conditions (MacDonald 1997, Labisky et al. 
1 999). The cyclic rising and falling of water levels in this marginal habitat influences 



2 
spatial movements (Sargent and Labisky 1995, Zultowsky 1992), habitat use (Hunter 
1990, Miller 1993) and reproductive phenology (Loveless 1959b, Richter and Labisky 
1985, Boulay 1992). 

Historically, the primary goal of deer managers was that of increasing herd 
productivity and health. Today, throughout much of the United States, managers have the 
task of controlling deer populations because inflated densities are exerting negative 
impacts on the landscape. However, in the Everglades, where white-tailed deer maintain 
low-density populations, managers must insure that deer populations persist. Thus, the 
maintenance of this deer population is one of the many goals of the large multi-agency 
research and restoration effort currently in progress in the Florida Everglades (Fleming et 
al. 1994, USGS 1997, DeAngelis et al. 1998). Part of this restoration effort is the 
development of the suite of simulation models. Across Trophic Level System Simulation 
(ATLSS), to predict and compare the effects of alternative hydrologic scenarios on this 
ecosystem. This suite of models, covering approximately 2.6 million ha, includes physical 
models (landscape hydrology and topography), process models (e.g., macro- and meso- 
invertebrates and vegetation), size-structured population models (e.g., fish and 
amphibians), and individual-based models (e.g., wading birds, white-tailed deer, and 
Florida panthers) designed to work interactively. 

In this dissertation, I explored movement patterns of white-tailed deer in the wet 
prairie/tree island habitat of the Florida Everglades. An individual-based spatially explicit 
(IBSE) simulation model was developed to simulate their movement patterns under 
normal and high water conditions. This model was designed to predict changes in the 



3 
movement patterns of the deer population under extreme flood conditions and alternative 
water management scenarios. 

1.1. Simulation Models as Research Tools 
Simulation models are important tools in wildlife ecology and conservation, and 
their use is increasing continuously. Computer simulations enable scientists to model the 
effects of environmental catastrophes or management strategies on target populations 
without conducting expensive or difficult field experiments. Early population simulation 
models ranged from simple growth models, such as logistic growth (Pearl and Reed 1920, 
Renshaw 1990) to stage- or age-based matrix models (Leslie 1945, Lefkovitch 1965). 
More recent population models incorporated a spatial component, such as spatial 
dispersion models (Skellam 1951) and metapopulation models (Levins 1969, Hanski and 
Gilpin 1996). hi the continuing evolution of simulation models, individual-based models, 
those using individuals as the basic unit (DeAngelis and Gross 1992, Grimm 1999), are 
the current state of the art. Widiin this large class of models, IBSE models are used to 
simulate individual movement processes and interactions over a heterogeneous landscape. 
This ability to model interactions among individuals and interactions between individuals 
and their environment provides insight into many ecological processes (Huston et al. 
1 988, Ims 1 995). Furthermore, these models are used to make or defend management 
decisions (DeAngelis and Gross 1992, Bart 1995, Conroy et al. 1995, Dunning et al. 
1995, Turner et al. 1995). As computing power and speed increase and computer costs 
decrease, more complex IBSE models become feasible. 

In individual-based simulations, in which each individual in a population is 
monitored, stochastic decision rules are developed to control the behavior and choices of 



4 
each individual. These models are particularly advantageous when studying populations 
with few individuals as well as when the study of individual behavior is important. 
Spatially explicit models allow simulation over a heterogenous environment, making it 
possible to define spatial relationships among habitat patches and other landscape 
features such as boundaries and corridors; therefore, the effect of a heterogenous 
environment on the organism of interest can be investigated. Saaremaa et al. (1988: 125) 
described the advantages of models using artificial intelligence as "(a) studying 
population processes based on individual levels of behavior, (b) modeling spatial 
heterogeneity, (c) building event-driven models, (d) providing a conceptual clarity to 
model construction, (e) and providing a structure equally well suited to simulating 
resource management." hitertwining animal movement dynamics and spatial patterns to 
reveal the larger picture can be accomplished with simulation models. Furthermore, these 
models comply with two basic doctrines of biology: that individual organisms are 
represented rather than being combined and represented by one variable (i.e., population 
size), and that these models distinguish among the locations of individuals (Huston et al. 
1988). 

Early simulation models of individual animal movements were developed using 
random walks and correlated random walks (Rolfe and Davenport 1969, Siniff and lessen 
1969, Holgate 1971, Bovet and Benhamou 1988). Effects of communication between 
individuals on movement patterns also have been explored. Montgomery (1974) 
expanded Siniff and Jessen's (1969) model to include the impact of communication (i.e., 
tactile, visual, scent, and vocal) among red fox (Vulpes vulpes) dyads on home range 
formation. Lewis and Murray ( 1 993) modeled territory formation and location of wolf 



(Canus lupus) packs as a function of scent marks left by neighboring packs and deer 
densities in the area. 

Recently, simulation models have been used to explore the effects of spatial 
heterogeneity on the dynamics and movements of animals. Effects of various timber 
harvesting schemes on Bachman's sparrow (Aimophila aestivalis) populations in the 
southeastern U.S. were simulated and evaluated (Pulliam et al. 1992, Liu 1993, Liu et 
al.l995). A model developed for the California spotted owl (Strix occidentalis caurina) 
explored the effects of habitat connectivity, quality, and quantity on population dynamics 
(Vemer et al. 1992). Turner et al. (1994) developed a model to explore movements of 
ungulates in Yellowstone National Park in response to fire. Riesenhoover et al. (1997) 
designed a simulation model to predict impacts of alternative deer management strategies 
on a population. Cramer (1999) developed an IBSE model to predict movements of 
Florida panthers in north Florida, should a reintroduction program be enacted. Although 
these simulations are predictive and often are not fially validated, they may still aid in 
understanding the dynamics of species and landscape interactions. 

The increasing reliance of management decisions on simulation models drives the 
necessity to develop tools to adequately calibrate and validate these models. Most 
individual-based models incorporate a large number of parameters (Grimm 1999). Some 
model parameters, such as number of offspring or survival rate, are estimated from 
published values, hi contrast, parameters characterizing movement patterns of individuals 
in a simulation rarely can be estimated from published values or even derived from 
measurable variables on study animals. These parameters (e.g., distance an individual can 
'see' when making a movement decision or the effect of previous movements on the 



6 
current movement decision) are either difficult or impossible to estimate from field data. 

However, the best-fitting movement algorithms and associated parameter values can be 
determined by evaluating discrepancies in measurable outcomes (e.g., home range size) 
between study animals and simulated animals. 

Bart (1995) and Conroy et al. (1995) suggested guidelines for model development 
and testing that included the need for clearly stated model objectives, a description of the 
model structure, and a sensitivity analysis to assess effects of parameter uncertainty on 
model outputs. In addition, model development also requires verification, calibration, and 
validation. As defined by Rykiel (1996), verification is a demonstration that the model 
form is correct, calibration is the estimation and adjustment of model parameters to 
improve agreement between model output and observed data, and validation is a 
demonstration that a model possesses the accuracy required for its intended applications. 

Although individual-based models ought to be more testable than state-variable 
models (Murdoch et al. 1992), only 36% (18 of 50) of the individual-based modeling 
papers reviewed by Grimm (1999) explicitly discussed validation or corroboration of the 
presented models. Statistical tools for validation of simulation models have been 
developed primarily in two fields of research: ecological process and population models 
(e.g.. Van der Molen and Pinter 1993, Rykiel 1996) and operations research and industrial 
engineering settings (e.g., Sargent 1984, Kleijnen 1987). 

1.2. Objectives 
The main objective of this dissertation was to develop an IBSE simulation model 
of movement patterns of adult white-tailed deer in the Florida Everglades. The model 
provides a means of exploring patterns of spatial use of deer in response to environmental 



7 
catastrophes (e.g., tropical storms) and to different management regimes (e.g., water 
control). Furthermore, the statistical methodologies used to calibrate and validate this 
IBSE model provide a foundation for the development of future simulation models. 

The specific objective of the simulation model was to predict how temporal 
landscape changes (i.e., rising and falling water levels) affect movement patterns of deer 
in the Florida Everglades. The simulation model was calibrated with radio-telemetry data 
collected from 1989 to 1992 imder dry-to-normal hydrological conditions. The same 
simulation model also was run under flood conditions, like those experienced during the 
flood that began in the fall of 1994, to evaluate the changes in movement patterns during 
an environmental catastrophe. In the development stages of this model, several calibration 
issues were addressed: (1) development of an approach to test the IBSE model relative to 
observed data with the use of discrepancy measures, (2) development of an effective 
approach for calibrating an IBSE model with sequential experimentation, and (3) 
evaluation of the predictive abilities of an IBSE simulation with predictive p-values. The 
model was validated with radio-telemetry data collected just prior to and during the flood 
of 1994-95. 

1.3. Dissertation Structure 

In Chapter 2, the Everglades ecosystem and the study area are described. In 
Chapter 3, the white-tailed deer calibration data are discussed in detail. The statistical 
techniques employed to calibrate the IBSE model and details of the fmal model are 
discussed in Chapter 4. In Chapter 5, the white-tailed deer validation data are presented 
and in Chapter 6, details of model validation are discussed. Conclusions and implications 
of the simulation results are discussed in Chapter 7. 



CHAPTER 2 
EVERGLADES ECOSYSTEM AND THE STUDY AREA 



Understanding the ecosystem under consideration is essential prior to simulation 
development. In this chapter, the Everglades ecosystem and the study area are discussed. 
Development of the temporal-spatial hydrology map is described. 

2.1. The Everglades Ecosystem 
2.1.1. Climate and Topography 

The Everglades ecosystem is characterized by a subtropical climate with 
alternating dry winters (November-April) and wet sunmiers (May-October). Mean 
monthly temperature ranges from 14 C in January to 28 C in August. Mean annual 
precipitation is 136 cm, two-thirds of which falls between May and October (Duever et 
al. 1986). The onset, duration, and intensity of the wet seasons are highly variable; thus, 
periods of either drought or flooding occur. Tropical cyclones (hurricanes and tropical 
storms) occur in this region of Florida at a rate of one every 3 years (Gentry 1984), and 
often exacerbate the severity of floods. Frost occurs infrequently, and a severe freeze 
occurs at a rate of one every 10 years (Drew and Schomer 1984). • 

The Everglades region is nearly flat, with an overall gradient on the order of 2 
cm/km in a north-south direction with steeper gradients at smaller spatial scales 
(Gunderson 1994), and is characterized by a southwestward sheet flow of water (Duever 



9 
et al. 1986). The range of elevations between the lowest and highest vegetation 

communities is approximately 1.5 m (Gunderson 1994). 

2.1.2. Flooding and Water Control 

The historic Everglades, a 3.6 million ha mosaic of marsh, slough, tree islands, 
and pinelands, extended from central Florida (Kissimmee Chain of Lakes) southward to 
the Florida Bay. "Replumbing" of the Everglades watershed began with the Swamplands 
Act of 1850, which authorized the transfer of 8.1 million ha of the Everglades to the state 
of Florida for the purpose of drainage and reclamation. In the 1880s, a millionaire 
entrepreneur purchased and drained more than 20,000 ha in the Kissimmee basin and 
built the first canals through the Everglades, demonstrating that the land was very 
productive and could be lucrative for agriculture (Blake 1980). To control the impacts of 
devastating floods and hurricanes on human populations and to further agricultural 
production, drainage of the Everglades and flood control measures on Lake Okeechobee 
continued into the early 1900s. The Central and Southern Flood Control District, later 
renamed the South Florida Water Management District (SFWMD), was formed in 1949, 
consolidating water management functions into one entity. Between 1950 and 1973, the 
SFWMD and the Army Corps of Engineers constructed a network of canals, pimips, and 
other water control structures. In the northern Everglades, the Water Conservation Areas 
were created to hold water away from the populated coastal areas and retain it for 
agricultural and municipal needs (Light and Dineen 1994). During periods of high 
rainfall, overflows from these areas were released southward often creating artificially 
high water levels in the Everglades National Park and surrounding protected areas. 



^klW.;> 10 



Approximately half of the original Everglades ecosystem remains today (Davis 
and Odgen 1994), but, in many places, the hydrologic regimes bear little resemblance to 
the historic predrainage flows (Light and Dineen 1994). Hydrology is the most important 
force shaping the Everglades, and it is the force that was most altered and has most 
affected the remaining system (Brandt 1997). Water control measures have exacerbated 
the effects of floods and droughts in the remaining natural system, and changes in 
hydroperiod length and intensity have altered vegetative communities. Modifications in 
hydrologic patterns have contributed to changes in plant communities, changes and 
decreases in wildlife populations, and changes in the historic fiinctioning of the 
Everglades (Loveless 1959a, Alexander and Crook 1984, Davis et al. 1994, Odgen 1994). 

2.2. Study Area 
The 30,000 ha study area (Fig. 2. 1 ) is located in the wet prairie/tree island 
ecosystem that extends fi-om the Stairsteps Unit of the Big Cypress National Preserve 
(BCNP) south into Everglades National Park (ENP). It is bounded on the north by Loop 
Road, on the west by Lostmans and Dayhoff Sloughs, and on the east and south by Shark 
River Slough. The habitat map (Fig. 2.2) was developed by Miller (1993); it depicts ten 
habitats (Table 2.1), using 20-m x 20-m pixels (referred to as "20-m pixels") with an 
estimated accuracy of 80.4%. Miller (1993) discussed the details of development of this 
map and its accuracy evaluation. 
2.2.1. Vegetation Classification and Hydroperiod Length 

Soil depth and type, hydroperiod (length of annual inundation), and fire are the 
primary factors in the development of plant occurrences in the wet prairie habitat of the 
Everglades (Duever 1984). Various vegetation classifications of the Everglades region are 



11 



reported in the literature (see Olmsted and Armentano [1997] for summary). The 
vegetation classification scheme used in this study follows the broad classifications of 
Duever (1984): forested uplands, non- forested wetlands, and forested wetlands. 




kilometers 



Figure 2.1. Location of study area within Big Cypress National Preserve (BCNP) and 
Everglades National Park (ENP), Florida. The study area is marked by the hashed lines. 



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12 



i 




V- 



■ ■■.m.isi''- I' ■ ■ / 



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4 



^* 






16 Kilometers 



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A/ BCNP / ENP boundary 

Habitat 

[ I Wet Prairie 

[ I Herbaceous Prairie 

1^1 Tree island 

p I Willow/dense sawgrass 

I i Dwarf cypress prairie 

\ I Cypress strand 

I I Pine 

m IVIangrove/prairie transition 

^B IVIangrove 




Figure 2.2. Habitat within the study area of BCNP and ENP, Florida. Map developed by 
Miller (1993). 



Table 2.1. Areal coverage of the habitats in the study area, BCNP and ENP, Florida [after 
Miller (1993)]. 





Area 




Habitat 


(ha) 


(%) 


Wet prairie 


21758 


62.9 


Herbaceous prairie 


5001 


14.5 


Tree islands 


2201 


6.4 


Willow/dense sawgrass 


1469 


4.2 


Dwarf cypress prairie 


2045 


5.9 


Cypress strand 


399 


1.2 


Pine 


143 


0.4 


Pine with dwarf cypress 


248 


0.7 


Mangrove/prairie transition 


568 


1.6 


Mangrove 


735 


2.2 



2.2.1.a. Forested uplands 

Hardwood tree islands, including hardwood hammocks and bayheads, account for 
approximately 6.4% of the study area (Miller 1993). Many of these tree islands are 
characterized by an elongated shape, as formed by the flow of surface water, although 
some in the drier prairies have a more rounded shape. Size of tree islands in the study 
area is variable (0.04-208 ha), but most (83%) are <1 ha (Fig. 2.3). Tree islands have a 
closed dome canopy of 6-20 m high. 

Hardwood hammocks are elevated above the surrounding prairie ^ 1 m, often on a 
bedrock outcrop (Craighead 1984). Hammocks are composed primarily of flood 
intolerant species including live oak (Quercus virginiana), wild tamarind (Lysiloma 
latisiliqud), gumbo limbo (Bursera simaruba), and strangler fig (Ficus aurea) (Duever et 
al. 1986). Bayheads are elevated above the surrounding prairie, but less so than hardwood 
hammocks, and are composed of flood tolerant temperate and tropical hardwoods 



14 





> 100.0 




10.0-100.0 




5.0-10.0 




3.0-5.0 


(0 


2,75-3.00 


^ 


2.50-2.75 


0) 
N 


2.25-2.50 




2.00-2.25 




1.75-2.00 


^ 


1.50-1.75 


(1) 


1.25-1.50 


1- 


1.00-1.25 




0.75-1.00 




0.50-0.75 




0.25-0.50 




0.00-0.25 




200 



800 



1000 



400 600 
Frequency 

Figure 2.3. Histogram of size of tree islands in the study area. Note that not all the widths 
of size categories for tree islands are the same. 



including red bay (Persea borbonia), wax myrtle (Myrica cerifera), cocoplum 
{Chrysobalanus icaco), and dalhoon holly (Ilex cassine). Common ground cover in tree 
islands includes royal fern {Osmunda regalis), swamp fern (Blechnum serrulatum), 
bloodberry (Rivina humilis), and greenbriar (Smilax spp.) (Duever et al. 1986). 

Inundation of hardwood hammocks is rare; however, partial inundation of 
bayheads is frequent. Between 1953 and 1978, the hardwood hammocks in the Pinecrest 
region of Big Cypress National Preserve were estimated to have been inundated only 2 
days (Gunderson and Loope 1982a). Schomer and Drew (1982) estimated a hydroperiod 
length of <1 month in hardwood hammocks. Shallow inundations lasting 0.3-1.5 months 
in hardwood hammocks and bayheads in BCNP were reported by Duever et al. (1986). 



15 

Slash pine (Pinus elliottii var. densa) forests are restricted to the extreme western 

edge of the study area. Pine forests have a grassy understory, commonly Muhlenbergia 
spp. and Andropogon spp.; drier forests often have a saw palmetto (Serenoa repens) 
understory (Duever et al. 1986). Hydoperiods are often non-existent, but if present, they 
average <2 months in length (Duever et al. 1986, Olmsted et al. 1980). 
2.2.1. b. Non-forested wetlands 

Non-forested wetlands, principally sparse sawgrass {Cladium jamaicensis) 
marshes and muhly grass {Muhlenbergia filipes) prairies, comprise 77.4% of the study 
area (Miller 1993). Sparse sawgrass marshes, which comprise 62.9% of the study area, 
are dominated by sawgrass, but also contain maidencane (Panicum hemitomon), 
spikerush (Eleocharis spp), muhly grass, as well as other grasses, sedges, and rushes 
(Duever et al. 1986). Patches of pickerelweed (Pontederia spp.) and arrowhead 
{Sagittaria spp.) are found in slight depressions in the marsh. Muhly grass prairies, also 
termed 'herbaceous prairies', constitute 14.5% of the study area and occur at slightly 
higher elevations than sparse sawgrass marshes (Miller 1993). These prairies support a 
higher diversity of herbaceous forbs and grasses, sedges, and rushes than sparse sawgrass 
marshes. 

Estimates of hydroperiod length in sparse sawgrass marshes and muhly grass 
prairie vary depending on geographic location and habitat classification. Annual 
hydroperiod estimates for sparse sawgrass in Shark Slough ranged from 6-12 months 
between 1953-1980 (Olmsted and Armentano 1997) and from 2.2-7.6 months in Taylor 
Slough between 1961-1977 (Olmsted et al. 1980). Annual hydroperiod estimates for 
muhly grass prairie ranged from 1.0-4.9 months in Taylor Slough between 1961-1977 



j....^; 



16 

(Olmsted et al. 1980), from 0.0-6.7 months in the Turner River area between 1964-1978 
(Gunderson et al. 1982), and from 1.0-3.6 months in Deep Lake Strand between 1973- 
1980 (Gunderson and Loope 1982b). Duever et al. (1986) defined wet prairies in BCNP 
to have hydroperiods of 1.7-5.0 months and freshwater marshes to have hydroperiods of 
7.5-9.0 months. Kushlan (1990) defined wet prairies to have hydroperiods of <6 months 
and sawgrass marshes to have hydroperiods of 6-9 months. 
2.2.I.C. Forested wetlands 

Willow (Salix caroliniana) forms dense thickets in flowing water sites, often 
surrounding tree islands and forming "tails" following the direction of water flow. Stands 
of tall (1-3 m) dense sawgrass are frequently found in association with willow thickets. 
These tall dense sawgrass strands frequently occur at slightly higher elevations than the 
surrounding prairie, and exhibit a reduced hydroperiod (Kushlan 1990). However, 
Olmsted and Armentano (1997) noted that east and west of Shark Slough, tall sawgrass 
strands are often found at lower elevations than the surrounding sparse sawgrass or 
spikerush marsh and exhibit hydroperiods of 6-8 months. In southern Taylor Slough, a 
willow/sawgrass stand had an estimated hydroperiod of 9.0-10.3 months between 1961- 
1977 (Olmsted etal. 1980). 

Cypress domes and strands (Taxodium spp.), which are restricted to the 
northwestern portion of the study area, occur in circular or elongated depressions in the 
bedrock and are characterized by an understory of herbaceous and woody species, such as 
bladderwort {Utricularia spp.), swamp fern {Blechnum serrulatum), buttonbush 
{Cephalanthus occidentalis) and willow {Salix caroliniana). Hydroperiods in cypress 
strands and domes average 8.3-9.7 months (Duever et al. 1984). Dwarf cypress forest is 



it 

an open forest with stunted, widely spaced cypress tress and a herbaceous understory. 
Hydroperiods in dwarf cypress forests range from 4-12 months (Flohrschutz 1978, 
Gunderson and Loope 1982a). 

Red mangrove {Rhizophora mangle) forests are restricted to the southwestern 
edge of the study area. These tidally submerged woodlands occur along the coast and 
inland along coastal rivers (Scholl 1968). Water in these swamps is <60 cm deep; and 
many interior areas are not inundated during an average high tide. The swamp floor is 
submerged entirely during extreme high tides, and many areas are exposed subaerially 
during low tide. 
2.2.2. Hydrology Patterns 

Hydrology patterns were inferred using historical data from hydrologic station P- 
34, which was located centrally in the study site in an area characterized as wet prairie or 
sparse sawgrass marsh (Fig. 2.4). During the period of record (1953-1995), data were 
missing for the following 4 months: October 1980, May 1991, January 1993, and 
February 1993. These missing data were estimated with an analysis of covariance, using 
water depths from a neighboring water gauge as the covariate. Three water gauges were 
identified as potential covariates (Fig. 2.4). NP-205, located 13 km northeast of P-34 in a 
drier prairie, had water levels strongly correlated with levels at P-34 (r=0.876, n=251); 
however, the period of record did not start until October 1974, and data were not 
available for January 1993 and February 1993. P-35 was located 18 km south of P-34 in 
southern Shark Slough; however, the correlation between water depths was not as strong 
(r=0.675, n=511). Measurement of water depths at P-36, located 17 km southeast of P-34 



■ V '^ . '. f^'i 



u 






X ^.; 
















- - ' - Jrt 



9 



NP-205 



>.r^^.* 






Shark^lough 



P-36 



• P-35 



10 



10 

95 



20 Kilometers 



/V BCNP / ENP boundary 

Habitat 

I I Wet Prairie 

I I Herbaceous Prairie 

Bl Tree island 

1^1 Willow/dense sawgrass 

Dwarf cypress prairie 

Cypress strand 
[ I Pine 

IB Mangrove/prairie transition 
^B Mangrove 




Figure 2.4. Study area with locations of neighboring hydrologic gauges, P-34, NP-205, P- 
35, and P-36. 



in central Shark Slough, began in February 1968 and the correlation with water depths at 
P-34 was the strongest (r=0.904, n=331). 

Based on the quantity of available data and strength of correlation, P-36 was 
chosen to predict water depths during the 4 missing months. The model included water 
depth at P-36 as a quantitative covariate with year and month included as qualitative 
factors. The inclusion of year and month improved the model fit (adjusted R^=0.817 for 
model with P-36 and adjusted R^=0.888 for model with P-36, year, and month). Other 
models that accounted for the temporal correlation of the data and the cyclical nature of 
the water depths were fit to the data. However, these models did not provide improved fit, 
possibly because of the intrinsic random nature of rainfall patterns and changes in water 
control measures during the period of record. 

Relative to four other gauging stations in wetland communities in ENP, P-34 had 
the lowest water levels and the shortest period of annual inundation; however, it also had 
the largest range of water level fluctuations (Gunderson 1990). Between 1954-1985, 
hydroperiods ranged fi-om 2-12 months with a historical mean of 6.6 months. No 
differences in hydropattem among community types were detected because of high year- 
to-year variability. 

From 1989 to 1992 (during the first field study), wet seasons appeared typical; 
however, dry seasons were much drier than average (Figs. 2.5 and 2.6). Hurricane 
Andrew, a relatively dry hurricane, moved through the study area in August 1992 and 
caused extensive damage to the tree islands by blowing down and completely defoliating 
most trees in its path (Labisky et al. 1999). The second field study was conducted from 
1993 to 1995. The fall of 1994 was extremely wet, with > 100 cm of rain occurring 



20 




o 



o 



O 
CO 



I 
O 



00 



00 
00 



CO 
00 



00 



00 
05 



00 
CD 
05 



CO 
CO 
C35 



00 

U IT) 

C3) 



CO 

U LO 

C35 



03 
CD 

>- 



o 

CO 
I 



o 

9 



o 

9 



<A 



e5 



m 



«S 



(lUO) |8A9| JGIBAA 



21 



90- 



60- 



^ 30i 

E 

S 

B 

> -30- 



-60- 



-90 



Observed monthly mean 
Historical monthly means 




1 I 1 1 1 1 1 

Jan 1989 Jan 1990 Jan 1991 Jan 1992 Jan 1993 Jan 1994 Jan 1995 

Year 

Figure 2.6. Mean monthly water levels recorded at P-34 hydrologic station from January 
1989 to December 1995 and historical monthly means from 1953-1985. Depths were 
predicted for May 1991, January 1993, and February 1993. 



between August and November, cuhninating with Tropical Storm Gordon in November 
1994 which contributed >20 cm of rain. Water levels remained high in the study area 
throughout 1995. 

A relative elevation map was created to simulate changes in water depths over 
time. Elevation of each habitat, relative to P-34, was derived from a literature review and 
estimation of annual hydroperiod length for various elevations (Table 2.2). The 20-m 
pixel elevation map was created from the habitat map and the estimated elevations (Fig. 
2.7). To allow for gradual changes in elevation on habitat edges, nearest-neighbor 
averaging was performed on the elevation map. 



4?- :'* 






22 



Table 2.2. Estimated elevation of each habitat, relative to P-34 hydrologic station", and 
estimated minimum, median, and maximum hydroperiod lengths (months per year) for 
each habitat. 



Habitat 


Estimated 

elevation relative 

to P-34 (cm) 


Estimated 
min 


hydroperiod 
med 


1953-1995 
max 


Wet prairie 





2 


7 


12 


Herbaceous prairie 


20 





3 


12 


Tree islands 


80 








2 


Willow/dense sawgrass 


-15 


5 


9 


12 


Dwarf cypress prairie 


5 





6 


12 


Cypress strand 


-10 


5 


9 


12 


Pine 


80 








2 


Pine with dwarf cypress 


30 








12 


Mangrove/prairie transition 


-5 


3 


8 


12 


Mangrove 


-20 


6 


12 


12 



P-34 hydrologic station was located in wet prairie habitat (Fig. 2.4). 



23 







s 







8 



A/ BCNP / ENP boundary 
Elevation classes (cm) 
I I -20 - -10 

-10-0 

0-10 

10-20 

20-30 

30-40 

40-50 

50-60 

60-70 

70-80 



16 Kilometers 



i 




Figure 2.7. Estimated elevation map (relative to P-34 hydrologic station) within the study 



area. 



CHAPTER 3 
WHITE-TAILED DEER MODEL CALIBRATION DATA 



The white-tailed deer population on the BCNP/ENP study site was the subject of 
intensive investigation from 1989-1992 (Boulay 1992, Sargent 1992, Zultowsky 1992, 
Miller 1993, Sargent and Labisky 1995, Labisky et al. 1999). The white-tailed deer data 
used for model calibration were analyzed to provide a starting point for the development 
of the simulation model. During the collection of this calibration data, environmental 
conditions ranged from mild drought to typical (Fig. 3.1). The simulation model 
developed in Chapter 4 reflects the movement patterns and habitat use dynamics explored 
in these analysis. 

3.1. Data Collection Methods 

White-tailed deer were captured exclusively by helicopter-netgunning (Barrett et 
al. 1982, Labisky et al. 1995). Each captured deer was aged, measured, and marked with a 
radio-transmitter/collar, equipped with motion-sensitive activity (2X signal pulse) and 
mortality (4X signal pulse) modes (Wildlife Materials, Inc., Carbondale, IL). Due to the 
inaccessibility of the study area, all radio-monitoring was conducted during daylight 
hours from a fixed-wing aircraft. To obtain unbiased temporal monitoring, radio-locations 
for each deer were evenly distributed among four daylight periods: sunrise to 2 hours 
post-sunrise, 2 hours post-sunrise to noon, noon to 2 hours pre-sunset, and 2 hours pre- 
sunset to sunset. By stratifying the radio-locations across the entire day, any diurnal 



-> » ^ V . t « 



90 



60- 



— 30 



i 



-30 



-60 



-90- 



Observed monthly mean 
Historical monthly means 



-1 

Jan 1989 



Jan 1990 



1 

Jan 1991 

Year 



25 




Jan 1992 



Figure 3.1. Mean monthly water levels recorded at P-34 hydrologic station, and historical 
monthly means from 1953-1985. Depths were predicted for May 1991. 



patterns present in movement characteristics or habitat associations would be equally 
represented and, thus, not impact annual and hydrologic season summary statistics. Each 
deer was located, on average, once every 5 days. The location error associated with aerial- 
based telemetry, estimated from blind placement of dummy radio-collars, was <30 m 
(Miller 1993). 

3.2. Data Summary Methods . . ^ ■ 

A deer was classified as a resident of either BCNP or ENP if > 75% of its radio- 
locations were located in one of the management units. Data were summarized on an 
annual basis with the annual cycle defmed to begin on April 1 of the calendar year. This 
annual cycle was divided into four periods based on reproductive phenology (Labisky et 
al. 1995). Weaning and pre-rut occur from April through June. Males are in rut and 
females in estrus from July through September. Post-rut and pregnancy occur from 



October through December, coinciding with the peak hunting season in BCNP. Fawning 
and antlerogenesis occur January through March, and all deer were assigned arbitrary 
birthdates of April 1. For the calibration data set, data were collected for 3 annual cycles 
[1989 (1 April 1989-31 March 1990), 1990 (1 April 1990-31 March 1991), and 1991 (1 
April 1991-31 March 1992)]. Deer included in an annual cycle were required to have a 
minimum of 50 radio-locations, be monitored for a minimum of 9 months during that 
annual cycle, and exhibit no dispersal movements. 

Differences in the measured parameters between hydrologic seasons also were 
estimated. Sufficient data were collected for 5 hydrologic seasons [89DRY (1 November 

1989 - 30 April 1990), 90WET (1 May 1990 - 31 October 1990), 90DRY (1 November 

1990 - 30 April 1991), 91WET (1 May 1991 - 31 October 1991), and 91DRY (1 
November 1991 - 30 April 1992)]. Deer included in these analyses were required to have 
been monitored for a minimum of 2 sequential hydrologic seasons and exhibit no 
dispersal movements during those seasons. Each included deer had a minimum of 30 
radio-locations and was monitored for a minimum of 5 months in each season. That 
condition was relaxed in 91 DRY to a minimum of 24 radio-locations and 4 months of 
observation because radio-monitoring ended on 31 March 1992. 

3.2.1. Annual Cycles 

Annual home range size was calculated using the 95% fixed kernel estimator with 
least squares cross validation (Silverman 1986, Worton 1989, Seaman and Powell 1996). 
Distance between centers of annual home ranges was calculated to access the degree of 
site fidelity. Mean distance between radio-locations for each deer was used as a proxy for 
the distance that a deer traveled during a 5-day interval. This statistic cannot be used as a 



27 

measure of the total distance that a deer traveled over a 5-day interval, but can be used as 

an indicator of the minimum distance a deer traveled over 5 days. Percentage of radio- 
locations in each habitat was used to establish habitat selection patterns. Sample means 
were weighted to account for deer with multiple years of observations. 

Resource selection was evaluated using chi-square analyses (Neu et al. 1974, 
Manly et al. 1993) for sample design II (multiple observations on same individual, 
assume same habitat availability for all individuals) and sample design III (multiple 
observations on same individual, estimate habitat availability for each individual) as 
defined by Thomas and Taylor (1990). To insure deer with multiple years of observation 
did not unduly influence summary statistics, 1 year of observational data from each deer 
was randomly selected for inclusion into these analyses. The original study and deer 
captures focused on tree islands and prairies of the study area; therefore, the few deer 
spending a large portion of their time in the pine, cypress, and mangroves were not 
included in these analyses. Separate summary statistics were calculated for females and 
males. 

For the sample design II analyses, habitat availability was assumed equal for all 
deer. After removing pine, cypress, and mangrove areas from the map, wet prairie, 
herbaceous prairie, tree islands, and willow/sawgrass accounted for 72%, 16%, 7%, and 
5% of the study area, respectively. The notation used for the habitat analyses was: 
7t j = known proportion of habitat /' in the study area, 
Uy = number of observations of the/'' animal in the /"■ habitat, 
Mj+ = total number of observations of all « animals in the /■"' habitat, 
u+j = total number of observations of the/'' animal in all habitats, and 



U++ = total number of observations. 
Selection ratios for each habitat were calculated. Each ratio was proportional to the 
probability of the given habitat being utilized, assuming the individual had unrestricted 
access to the entire distribution of habitats. The selection ratio and associated variance for 
eachhabitat for this population of deer was estimated with ■ > ., ' i ^ ; ,, 



«; 



7+ 



varl 



K) = 



["(-Ml 

7=1 


n 


2 



Simultaneous Bonferroni confidence intervals for the selection ratios were calculated 
using an a-level of 0.05. Those confidence intervals not including 1 indicated either 
selection for (ratio >1) or against (ratio <1) a particular habitat, and confidence intervals 
including 1 indicated no evidence of selection for or against a particular habitat. A second 
sample design II analysis was performed, using the percentage of each habitat contained 
inside the 100% minimum convex polygon (MCP) home range for each deer, rather than 
the number of radio-locations in each habitat. 

For the sample design III analyses, habitat availability was estimated individually 
for each deer using the proportions of habitats contained inside the 100% MCP home 
ranges. Notation was the same as defined above for design II except that tI; was the 
known proportion of habitat i contained in the home range of individual/. Population 
selection ratios and associated variances for each habitat were estimated using 



29 



M.x 



^i = — 






Kj = 



7=1 / 



Simultaneous Bonferroni confidence intervals for these population selection ratios using 
an a-level of 0.05 also were calculated. 
3.2.2. Hydrologic Seasons 

For each deer, home range size for each of the hydrologic seasons was calculated 
using the 95% fixed kernel estimator with least squares cross validation. Mean distance 
between radio-locations for each deer served as a proxy for the distance a deer traveled 
during a 5-day interval. Mean home range size and distance between consecutive radio- 
locations and their standard errors were estimated using the number of seasons each deer 
was in the sample population as weights. Differences between the WET and DRY 
seasons were tested using a mixed model analysis with deer as a random effect and 
hydrologic season as a fixed effect. 

Percentage of radio-locations occurring in each habitat was used to establish 
differences in seasonal habitat selection. Deer observed in pine, cypress, or mangrove 
habitats were not included in these analyses. The generalized Cochran-Mantel-Haenszel 
test (Birch 1965, Agresti 1990) was conducted for each gender to test for an overall 
association between hydrologic season and habitat selection. Additionally for each 



30 

deer, a chi-square test was performed to test the hypothesis that there was a difference in 

the distribution of radio-locations across habitats between WET and DRY seasons. 

3.3. Data Summary 

Estimated white-tailed deer densities for 1 990- 1 992 were 3 .65 (se= 1 .47) deer/km^ 
for the hunted BCNP population and 4.68 (se=l .00) deer/km^ for the non-himted ENP 
population (Labisky et al. 1995). The data set used for model calibration included 
yearling and adult deer that were captured, radio-collared, and monitored between 1989 
and 1992. Data from 46 yearling or adult deer were used for initial model calibration 
(Appendix A). Twenty- four deer were radio-monitored for 1 year, 18 deer for 2 years, and 
10 deer for 3 years. Ten deer were radio-monitored for 2 hydrologic seasons, 15 deer for 3 
seasons, 12 deer for 4 seasons, and 6 deer for 5 seasons. 
3.3.1. Annual Cycles 

The mean annual home range size of females was 271 ha (se=20, n=29), with a 
range from 90 ha to 600 ha. Male home ranges were slightly larger (316 ha, se=49, n=17) 
ranging from 102 ha to 1086 ha. Distance between consecutive home range centers was 
similar for both genders; females had a mean distance of 307 m (se=53, n=17) and males 
had a mean distance of 243 m (se=56, n=9). 

Time intervals between radio-locations ranged from 1 to 14 days; however, many 
(46%) were 5 days in length. To ensure the length of the measurement interval was not 
influencing the straight-line distance between locations, an analysis of covariance 
(ANCOVA) was performed. Distance between consecutive measurements had a skewed 
distribution (Fig. 3.2) and was log-transformed prior to analysis. In the ANCOVA model, 
the fixed effects were year ( 1 989, 1 990, 1 99 1 ), days between radio-locations (linear 



tl 



0.25n 



0.20- 



§ 0,15- 

cr 

o 

> 

CD 

0.10- 



0.05- 



0.00- 




(a) 



I 1 1 1 1 1 1- 

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 



Distance, m 



0.25n 



0.20- 



>> 

o 

c 
<u 

S'o.15- 

0) 

> 

TO 

0^ 0.10- 



0.05- 



0,00- 




(b) 



1 1 1 1 1 1 1- 

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 



Distance, m 



Figure 3.2. Histogram of straight-line distances (m) between consecutive radio-locations 
for (a) female and (b) male white-tailed deer. 



m 

covariate), and their interaction; the random effect was deer. Using an a-level of 0.05, the 
fixed effects did not have a significant effect on distance between consecutive 
measurements (Table 3.1). The mean distance between consecutive locations was 686 m 
(se=29, n=29) for females and 779 m (se=79, n=17) for males. Most distances were <750 
m (65%) and nearly all <1500 m (90%), but deer occasionally were recorded traveling 
longer straight-line distances (maximum observed distance= 10240 m). 



Table 3.1. Results from the analyses of covariance for log-transformed distance between 
consecutive radio-locations for female and male white-tailed deer. 



Fixed Effect 


df numerator 


df denominator 


p-value 


Female 








YEAR 


2 


3034 


0.4366 


DAYS 


1 


3034 


0.0766 


YEAR*DAYS 


2 


3034 


0.6011 


Male 








YEAR 


2 


1715 


0.1924 


DAYS 


1 


1715 


0.5992 


YEAR*DAYS 


2 


1715 


0.1596 



Based on simple summaries of percentage of occurrances in each habitat (Table 
3.2), females appeared to select for wet prairie more strongly than males, and males 
appeared to select for tree islands and willow/dense sawgrass more strongly than females. 

Habitat-use patterns were evaluated quantitatively using selection ratios. When 
evaluating habitat selection based on the choice of a home range (100% MCP), assuming 
equal availability of habitat for all individuals, females exhibited no significant selection 
for or against any habitat since all the confidence intervals included 1 (Table 3.3). 
However, males selected home ranges with less wet prairie and more willow/dense 
sawgrass than expected, based on availability in the study area (Table 3.3). When the 



33 

selection ratios were calculated using radio-locations and assumed equal habitat 
availability for all individuals, both females and males demonstrated habitat preferences 
(Table 3.4). Both genders selected against wet prairie, had no selection for or against 
herbaceous prairie, and selected for tree islands and willow/dense sawgrass; however, 
males tended to exhibit stronger selection for or against a particular habitat than females, 
as evidenced by the more extreme selection ratios (i.e., selection ratios farther from 1). 
These selection ratios were more extreme than those based on selection of home range 
area (Table 3.3), which was expected because the analysis based on home range areas 
assumed equal use of all the area contained inside the home range. Similar selection 
trends were observed when habitat availability was estimated separately for each 
individual using 100% MCP (Table 3.5). Both females and males selected against wet 
prairie, selected neither for nor against herbaceous prairie, and selected for tree islands 
and willow/dense sawgrass inside their home ranges. These results were similar to 
Miller's (1993) fmdings. 



Table 3.2. Mean percentage of radio-locations in each habitat for the study sample of 

white-tai led deer in BCNP and ENP, April 1989 to March 1992. 

Habitat Female' Male 



Wet prairie 


53 


(4)" 


25 


(4) 


Herbaceous prairie 


17 


(3) 


20 


(3) 


Tree islands 


17 


(2) 


33 


(4) 


Willow / dense sawgrass 


9 


(1) 


18 


(2) 


Dwarf cypress prairie 


1 


(1) 


2 


(2) 


Cypress strand 


<1 


(<1) 


1 


(1) 


Pine 


<1 


(<1) 


<1 


(<1) 


Mangrove 


2 


(2) 


1 


(1) 



" Sample sizes: female (29), male (17). 
'' Standard error in parentheses. 



M 



Table 3.3. Selection ratios and 95% Bonferroni confidence intervals" using the design II 
analysis for habitat inside 100% MCP for the study sample of white-tailed deer in BCNP 

an d ENP, April 1989 to March 1992. 

Habitat Female'' Male 

Wet prairie 1.05 (0.90,1.20) 0.77 (0.56,0.98) 

Herbaceous prairie 0.88 (0.08,1.39) 1.51 (0.94,2.08) 

Tree islands 0.74 (0.35,1.13) 1.67 (0.68,2.66) 

Willow/dense sawgrass 1.02 (0.58,1.46) 1.73 (1.13,2.33) 

" Confidence intervals that do not include 1 indicate a selection against (selection ratio 
<1) or a selection for (selection ratio >1) a given habitat. 
*" Sample sizes: female (26), male (12). 



Table 3.4. Selection ratios and 95% Bonferroni confidence intervals" using the design 11 
analysis for radio-locations for the study sample of v^^hite-tailed deer in BCNP and ENP, 

A pril 1989 to March 1992. 

Habitat Female'' Male 

Wetprairie 0.75 (0.59,0.91) 0.35 (0.18,0.51) 

Herbaceous prairie 1.15 (0.60,1.70) 1.14 (0.88,1.69) 

Tree islands 2.41 (1.47,3.34) 5.29 (3.64,6.90) 

Willow/dense sawgrass 2.14 (1.53,2.76) 3.96 (2.95,4.94) 

" Confidence intervals that do not include 1 indicate a selection against (selection ratio 
<1) or a selection for (selection ratio >1) a given habitat. 
'' Sample sizes: female (26), male (13). 



Table 3.5. Selection ratios and 95% Bonferroni confidence intervals" using the design III 
analysis for the study sample of white-tailed deer in BCNP and ENP, April 1989 to 
M arch 1992. 

Habitat Female'' Male 

Wetprairie 0.72 (0.62,0.83) 0.45 (0.30,0.59) 

Herbaceous prairie 1.28 (0.96,1.60) 0.79 (0.45,1.12) 

Tree islands 3.16 (1.97,4.35) 3.19 (1.67,4.71) 

Willow/dense sawgrass 2.05 (1.13,2.97) 2.16 (1.44,2.89) 

" Confidence intervals that do not include 1 indicate a selection against (selection ratio 

<1) or a selection for (selection ratio >1) a given habitat. 

'' Sample sizes: female (26), male (12). 






35 

3.3.2. Hydrologic Seasons 

Mean WET season home range size of females (n=26) was 2 1 1 ha (se= 1 7) and 
was significantly different (p=0.0025) from the mean DRY season home range size of 
303 ha (se=36). The mean WET season home range size of males (n=17) was 301 ha 
(se=48) and was significantly different (p=0.0007) from the mean DRY season home 
range size of 187 ha (se=36). 

Mean distance between consecutive radio-locations followed a pattern similar to 
home range sizes. Mean distance between consecutive radio-locations in the WET season 
for females (n=26) was 638 m (se=27) and was significantly different (p=0.0025) from 
the mean DRY season distance of 722 m (se=34). Mean distance between consecutive 
radio-locations in the WET season for males (n=17) was 866 m (se=67) and was 
significantly different (p=0.0007) from the mean DRY season distance of 664 m (se=81). 

There was no evidence of a change in habitat use between the hydrologic seasons 
based on radio-locations for females (Cochran-Mantel-Haenszel test, p=0.75, df=3, 
n=2702) (Table 3.6). Of the 24 females included in this analysis, only three had a 
significant association between hydrologic season and habitat (chi-square test, p<0.05, 
df=3), but there was no commonality in the associations between hydrologic season and 
habitat. There was evidence of a change in the distribution of habitat use based on radio- 
locations for males (Cochran-Mantel-Haenszel test, p=0.001, df=3, n=1498) (Table 3.6). 
During the DRY season, males increased their use of wooded areas (tree islands and 
willow/dense sawgrass) and decreased their use of wet prairie relative to WET season 
habitat use. Of the 1 1 males included in this analysis, six had a significant association 
between hydrologic season and habitat (chi-square test, p<0.05, df=3), and they typically 



36 



56 


(5) 


28 


(5) 


17 


(4) 


16 


(3) 


20 


(4) 


20 


(4) 


18 


(3) 


35 


(3) 


41 


(4) 


12 


(1) 


17 


(2) 


22 


(3) 



Table 3.6. Hydrologic season habitat use based on percentage of radio-locations in each 
habitat for the study sample of white-tailed deer in BCNP and ENP, November 1989 to 

March 1992. 

Female* Male 

Habitat WET DRY WET DRY 

Wet prairie 55 (5)" 

Herbaceous prairie 1 8 (4) 

Tree islands 17 (3) 

Willow/dense sawgrass 11 (1) 
" Sample sizes: female (24), male (11). 
^ Standard error in parentheses. 



followed the same trend of increased use of wooded areas and decreased use of prairie in 
the DRY season, relative to the WET season. 

3.4. Discussion 
3.4.1. Annual Cycles 

The most conspicuous observation regarding any of the spatial-use summary 
measures was the large variation among individuals and among years. Males tended to 
have slightly larger mean annual home ranges and mean straight-line distances between 
consecutive locations than females; however, this was negligible when individual 
variability was taken into account. This high variability among individuals may be due to 
a variety of factors such as resource availability (Byford 1969, Miller 1993), age (Gavin 
et al. 1984, Nelson and Mech 1984), concealment cover (Sparrowe and Springer 1970), 
weather (Michael 1970, Drolet 1976), and human disturbance (Sparrowe and Springer 
1970). Local population dynamics such as density and social structure also may influence 
spatial-use patterns (Sanderson 1966, Gavin et al. 1984, Zultowsky 1992, Miller 1993). 
These deer exhibited a high degree of site fidelity, as evidenced by the small shifts in 



annual home range centers, which measured <1 km for all deer. The strength of site 
fidelity in this population of deer during the time frame of the calibration data set also 
was discussed by Sargent (1992) and Zultowsky (1992). Labisky et al. (1999) noted the 
continuous maintenance of home ranges, even after the passage of Hurricane Andrew in 
August 1992. 

The most prominent difference between spatial-use patterns of adult females and 
males was habitat selection. Females were twice as likely as males to be radio-located in 
the prairie, and males were twice as likely as females to be radio-located in a tree island 
or willow/dense sawgrass areas. This differential preference between females and males 
as evidenced by percentage of radio-locations in each habitat also is supported by the 
magnitude of the selection ratios calculated using radio-locations in the study site (Table 
3.4). For many ungulates, differential use of food and cover resources by gender occurs as 
a result of differing energetic and reproductive strategies (Main and Coblentz 1990, 
Miquelle et al. 1992). Hydrophytic forbs (notably swamp lily, Crinum americanum), 
which contain high levels of crude protein (>15%) year-round (Loveless 1959a), 
comprised 68% of the annual diet of females in the study area (Hurd et al. 1995). Isolated 
patches of prairie that remain wet during the dry season support lilies and other forage 
important for pregnant and lactating does (Hunter 1990). Increased use of prairies also 
may provide protection against bobcat predation on fawns (Boulay 1992). Males consume 
a higher proportion of the woody browse and ferns found in the tree islands and wooded 
areas than females (Hurd et al. 1995). Males strive to maximize weight gain because 
increased body size leads to higher reproductive success (Clutton-Brock et al. 1982). Due 
to larger rumen size, males may require larger amounts of forage, but can subsist on 



31 

lower quality food (McCullough 1979, Shank 1982, Bowyer 1984, Beier 1987). 

Therefore, males focus foraging efforts on tree islands, which probably support higher 
forage biomass per unit area than other habitats (Miller 1993). 

Females showed no significant trends for selection of home range content; 
however, males selected home ranges containing less wet prairie and more herbaceous 
prairie and wooded areas. Due to the polygynous nature of white-tailed deer, females are 
organized into matrilineal groups and tend not to disperse as juveniles, whereas males 
disperse from the family group at sexual maturity and establish new home ranges 
(Marchington and Hirth 1984). Therefore, males had an opportunity to select home ranges 
containing a higher proportion of their preferred habitats. 
3.4.2. Hydrologic Seasons 

Females traveled farther and had larger home ranges in the dry season than the 
wet season, possibly because of limitations in nearby available forage during the winter 
drought. Typically, white-tailed deer concentrate activities when food is plentiful and 
expand activities when food is scarce (Byford 1969). However, no changes in the habitat- 
use patterns of females between the wet and dry seasons were evident. 

Males traveled more, had larger home ranges, increased their use of wet prairie, 
and decreased their use of tree islands in the wet season relative to the dry season. 
Because the wet season includes the rutting period, during which time males are 
searching for females to breed, they travel greater distances to find females and utilize the 
landscape matrix of wet prairie more heavily in those search efforts. During the seasonal 
hunt, which occurs during the early dry season, males, especially those in BCNP, may 
increase their use of wooded areas to obtain a higher degree of concealment cover. 



CHAPTER 4 

DEVELOPMENT, CALIBRATION, AND EVALUATION 

OF THE SIMULATION MODEL 



In this chapter, I present and demonstrate the approach developed to calibrate an 
IBSE simulation model. Specific issues with regards to model calibration are addressed 
and then introduced as steps of an iterative process to attain a satisfactory simulation 
model. Finally, parameterization of the final simulation model is described. I developed 
the simulation using C++ (Borland C++ Builder 3.0, Inprise Inc.) with object-oriented 
programming techniques. 

4.1. Approach and Technique 

Determining correct model form (verification) involves evaluating the conceptual 
structure and the transformation of the structure into computer algorithms (Bart 1995, 
Conroy et al. 1995, Rykiel 1996). Model structure is often visualized through flow charts 
(Fig. 4.1). Detailed literature review and analyses of additional data aid the verification of 
correct conceptual model structure. Assuming the model structure is correct, the 
calibration process consists of altering parameter values until the modeled system is 
represented adequately. Model calibration also may reveal algorithms in the simulation 
model that need to be modified if the optimum parameterization of the algorithm is not 
sufficient. Updating algorithms and parameter values is an iterative process, requiring 
constant reevaluation of the simulation model. 



39 



40 



Read in habitat and elevation maps, 
monthly water depths at gauging station 



J 



Initialize water depth map 



Generate starting locations for each deer 



Each deer evaluates surrounding pixels based on: 
habitat 
water depth 

location relative to home range 
etc. 



T 



Each deer chooses a new location and moves there 



I 



Each deer updates location coordinates 
and memory of past locations 




Update water 
depth map 




Figure 4.1. Simulation flow chart to aid in visualization of model structure. Example 
depicts white-tailed deer movement in the Florida Everglades. 



41 

During the development of this model building process, I chose to focus on 
several issues. Parameterization of the movement process is approached by quantitatively 
and visually evaluating various movement algorithms. An approach for evaluation of 
potential movement algorithms relative to the observed field data is presented. To address 
algorithm and parameter value evaluation, simulation experiments are conducted, and 
simulated and observed data are compared quantitatively with discrepancy measures. 
However, before quantitative model evaluation is performed, the amount of time (i.e., 
number of iterations) the simulation must run before meaningful testing can occur must 
be determined. Qualitative evaluation (e.g., visual comparison) also is an important 
component of model calibration. Once the simulated data approach the observed data, the 
robustness of the simulation to represent the observed data is evaluated. 
4.1.1. Parameterization of Animal Movement 

Observed movement patterns are a function of many possible factors, which vary 
from individual to individual. Some of these factors may include age, predator threat, 
availability of food and water, location of neighboring individuals (of the same or 
different species), surrounding micro- and macro-habitat, weather, time of year, and time 
of day. Differences in individual preferences and random chance also may influence 
movement decisions. Many of these potential influences can be measured (i.e., weather 
conditions and habitat availability), and potential relationships between these factors and 
the movement patterns can be explored (i.e., correlation analyses and habitat-selection 
ratios). However, often these factors cannot be measured on the scale appropriate for the 
parameters of interest, and some factors may be unmeasurable or unknown. ; 



' 42 

Radio-telemetry data collected from individual animals can provide some of this 

information (White and Garrott 1990). These data are used to evaluate individual patterns 

of movement, home range size and shape, and habitat use. However, these summary 

statistics are 'outcomes' resulting from the movement patterns generated by a multitude 

of factors. Statistical analyses can identify associations between the environmental factors 

and the measured outcomes. These associations help in formulating testable hypotheses 

regarding how environmental factors may affect movement patterns, and, thus, affect the 

measured outcomes. This approach is useful in developing a simulation of animal 

movement patterns. Based on knowledge of the natural history of the species and the 

results of the data analyses, rules to simulate movement patterns can be developed. These 

rules then can be tested by comparing the measured 'outcomes' from the real individuals 

and the 'outcomes' of the simulated individuals. 

Simulating animal movement paths is accomplished with any of several 

approaches. Vector-based models, in which a simulated individual chooses a movement 

direction and, often, a movement distance for each step, constitute one approach. The 

direction and distance for each move are chosen, based on those surrounding 

= environmental factors deemed important to movement decisions. Grid-based models, in 

which simulated individuals move among pixels on a grid superimposed over the 

landscape, constitute a second approach. These vector- or grid-based simulation models 

can be either deterministic or stochastic. Deterministic models are designed such that the 

individual always makes the 'best' movement decision (i.e., always moves in the 

direction of best habitat). In contrast, stochastic models use random draws from various 

probability distributions based on those factors that influence movement decisions, such 



43 

that individuals are most likely to make the 'best' choice. For the model presented in this 

study, I used the grid-based stochastic simulation approach. 
4.1.2. Measuring Model Fit 

Model fit is evaluated by comparing simulated outcomes of the model and 
observed outcomes of the field data. These quantities, often termed discrepancy measures 
(DMs), quantify the difference between a simulated data set and an observed data set and 
have the general form: * *•, 

d{x) = g{pix),0) 

where P{x) is a summary statistic for one run of the simulation with parameter set x, x is 
an element of X (the set of all feasible model parameters), and O is the summary statistic 
computed for the observed data (Van der Molen and Pinter 1993). The objective of model 
calibration is to minimize the DM(s). DMs may be calculated for summary statistics such 
as average home range size or the percentage of time individuals are located in specific 
habitat types. 

One family of DMs takes the form: 

d{x) = \p{x) - o\^ 

where p>0 (Van der Molen and Pinter 1993). For example, if p=l, D(x) is the absolute 
value of the deviation between simulated and observed summary statistics, and if P=2, 
D(x) is the squared deviation between simulated and observed summary statistics. 
Evaluation of summary statistics, such as mean annual home range size or mean distance 



u 



44 

between consecutive annual home range centers, is accomplished with this family of 
DMs. 

A DM useful for evaluating a set of n dependent outcomes, such as the percentage 
of radio-locations in each habitat, has the form: 



ow=i(^<^^-°''' 



/=i 



o. 



where (9, is the summary statistic for the observed data for the /"" outcome, P^(x) is the /"' 
summary statistic for a run of the simulation with parameter set x, and x is an element of 
X (the set of all feasible model parameters). This DM approximates a chi-square 
goodness-of-fit statistic with n-1 degrees of freedom where P^ix) and O^ are the 
percentage of occurrences in habitat / based on simulated and observed individuals, 
respectively. Mayer and Butler (1993), Power (1993), and Van der Molen and Pinter 
(1993) provide additional forms for discrepancy measures. 
4.1.3. Visual Assessment 

An additional component of model verification and calibration is the visual 
comparison of simulation output and observed data. Even if the discrepancy measures 
based on simimary statistics demonstrate that simulation output is comparable to 
observed data, movement patterns also must be visually realistic based on knowledge of 
the natural history and ecology of the species. 



45 
4.1.4. Experimental Design 

Simulation experiments are conducted to identify a set of algorithms and 
parameter values that minimizes discrepancies between simulated and observed data. In 
this setting, each algorithm and parameter value to be evaluated is a factor in the 
experiment, and an experimental unit (EU) is one run of the simulation model. When 
evaluating large numbers of model parameters, effects of each parameter on simulation 
outcomes can be complicated and difficult to identify. Factorial experiments allow for the 
simultaneous investigation of the effects of many factors (i.e., simulation model 
parameters). Moreover, the ensuing analysis of variance (ANOVA) of the simulation data 
can include interaction terms that explain the interrelationship among the simulation 
parameters. However, as the number of investigated factors increases, the number of EUs 
required to examine all factor combinations increases rapidly. For example, a factorial 
experiment having/? factors, each with k levels, requires If EUs for one replicate. 
Experimental designs have been developed that make efficient use of resources by 
requiring a minimal number of EUs. Response surface methodology (Khuri and Cornell 
1987, Montgomery 1991) also provides a collection of specific experimental designs and 
statistical techniques to facilitate the estimation of factor settings that optimize a response 
variable. 

Often a sequence of experiments is necessary to optimize simulation model 
algorithms and parameters, with the analysis of each experiment dictating the particulars 
of the following experiment. First-order designs are initial screening experiments used to 
estimate and test main effects and interactions among the factors. Common designs are 2'' 
factorials and fi-actions of 2'' factorials (Cochran and Cox 1957, Montgomery 1991). 



Fractional factorials reduce the number of required EUs using the assumption that higher- 
order interactions (i.e., 3- and 4-way interactions) are negligible. The response variables 
from each EU are analyzed using ANOVA. For the model development process presented 
in this study, the response variables are DMs (Section 4.1.2), and the goal of optimization 
is to attain values of these DMs close to zero. If an optimimi is not attained inside the 
initial experimental region, the method of steepest descent is used to establish parameter 
settings for a subsequent experiment more likely to contain a minimum (Khuri and 
Cornell 1987, Montgomery 1991). This process is repeated until a minimum is achieved, 
which results in a sequence of experiments. 

When statistical analyses indicate that the design settings are close to an optimum, 
additional experimentation is performed to identify a set of parameter settings that 
minimizes the DM (a local minimum). More specifically, a second-order design, 
estimating main effects, first-order interactions and quadratic effects, is often required to 
approximate the curvature of the true response surface. Common second-order designs 
are central composite designs, 3" factorials, and 3" fractional factorials (Cochran and Cox 
1957, Khuri and Cornell 1987). 
4.1.5. Simulation Burn-in Time 

The "bum-in" period (Fig. 4.2) is the number of iterations required for the 
simulation to reach a steady-state (Kleijnen 1987). A population-based stochastic model 
is said to have a statistically stationary state if the probability distribution of population 
size is constant over a long time interval (Nisbet and Gumey 1982). When generalized to 
all population- and individually-based simulation models, the bum-in period is completed 
when a statistically stationary state is reached by all relevant outcome measures. 



47 







Figure 4.2. Example of bum-in time estimation for a simulation outcome measured on an 
annual basis. Individual outcomes are plotted in grey; linear slope is significantly 
different from zero when estimated for all years (heavy solid black line) and not 
significantly different from zero when using data from years 2 through 10 (heavy dashed 
black line). 



Estimation of bum-in time is important for several reasons. First, if the goal of the 
modeling effort is to explore the impacts of perturbations on the simulation outcomes, the 
simulation must be in a steady-state before applying the perturbations. If it is not in a 
steady-state, the effects of bum-in and the perturbations on the simulation outcomes are 
confounded (i.e., confused and inseparable). Second, if the goal of the modeling effort is 
to explore impacts of introduction or reintroduction of a species in a particular geographic 
region, then determining if a steady-state is reached is essential. If it is determined that a 
steady-state is reached, estimating the time until that steady-state is reached is also 
important. 



48 

Bum-in time is estimated by running the simulation for an extended period of 

time and examining temporal trends and autocorrelations of simulation "outcomes" for 
each individual (Fig 4.2). The approach for this study utilizes repeated measures analyses 
to identify significant time trends in the summary outcome (Diggle et al. 1994, Littell et 
al. 1996, Vonesh and Chinchilli 1997). If no significant linear time trend over the entire 
simulation interval is present, bum-in time has no effect on that particular outcome. A 
significant linear time trend is evidence that simulation bum-in affects the outcome 
measure. In this case, the test for a linear trend is repeated using all the time intervals 
except the first. If the second test for a time trend is not statistically significant, bum-in 
time is established at one interval; otherwise, the linear trend test is repeated excluding 
the first and second time intervals. These steps continue until there is no longer a 
significant linear time trend. If the simulation has not reached a steady-state until the end 
of the simulated time period or never reaches a steady-state (i.e., simulation bum-in time 
is equal to or longer than the time period of the simulation), further exploration of bum-in 
time and the form of the simulation algorithms is necessary. For each test for linear trend, 
an a-level of 0.01 was used. Because of multiple and sequential testing, this slightly more 
conservative a-level was used to reduce Type I error rates. 
4.1.6. Final Model Evaluation 

In all model-building exercises, evaluating goodness-of-fit of the final model is 
cmcial. For models such as regression, analysis of variance, and generalized linear 
models, fit often is evaluated with the coefficient of determination (R^), Akaike's 
Liformation Criterion [AIC (Akaike 1 974)] , and chi-square goodness-of-fit tests. 
However, these tools are not applicable for Monte Cario simulations, such as the IBSE 



' -'v , 



49 

simulation developed in this dissertation. To evaluate the simulation results, I test the 

likelihood of values of the observed outcomes arising as realizations of the posited 
stochastic model using estimated p-values from an estimated predictive distribution (Rao 
1977, Bj0mstad 1990, Gelman et al. 1995). First, the general approach is described, and 
then the adaptation of this method used for evaluating the IBSE simulation model is 
presented. 

Let yi, y2, y^, ■ ■ . , y„ be the observed data, where each y-^ is either a vector or a 
scalar variable and n is the number of observations. Also let be the vector of unknown 
parameters in the model, andj{yi,y2,y^, . . . ,>;je) be the density (i.e., the joint 
distribution of y^,y2,yi, .. .,y„ given 6). Inferences regarding some subsequent 
observation, y*, can be made using the predictive density function (PDF): 

/^ * h '>'2 '>'3 '•••'>'„' ^) 

If 6 is known then the PDF provides all the information regarding inferences on>'*. If 6 is 
unknown, one approach to making inferences on^'* is to estimate and substitute the 
estimate for in the PDF. The parameter, 0, can be estimated from 

/(yi^yi^yi'-'-^yJ^) 

usmg maximum likelihood or some other estimation method. Using this estimated value 
for 0, the estimated predictive density function (EPDF) 

f(y*\yi'y2'y3'---'yn'^) 

can then be used to make inferences about >'*. Using the EPDF with a known form and an 



so 

estimated to make inferences about 7* is misleadingly precise and results in predictive 
p-values that are more extreme than if were known (Aitchison and Dunsmore 1975). 
For the simulation model developed in this study, >'„ >'2, yj, ■ • • ,yn represent the 
summary outcomes (e.g., mean annual home range size and mean percentage of 
observations in each of the habitats) from n runs of the simulation model, is the vector 
of unknown model parameters (e.g., number of steps per day, relative affinities for 
habitat, and relative affinities based on water depths), and y* is the summary outcome 
fi-om observed field data. Of interest is the likelihood that the value ofy* could have 
arisen as an outcome of the simulation model. Assuming >'* is independent of>'i,>'2,>'3, . . 
. , >■„, the EPDF simplifies to 

f{y*\e) 

where $ is provided by the calibration process. The likelihood that the value of >>* could 
have arisen from the posited simulation model can be measured by the tail-area 
probability: 

min[pr(y < >; * 1^), Pr(y > >> * 1^)] 

Because the empirical form of the EPDF is unknown, the predictive p-value is estimated 
by an approximate distribution obtained through Monte Carlo simulation. Multiple runs 
of the IBSE simulation model are conducted and the distribution of the simulated 
outcomes is used to estimate the tail-area probability (Fig. 4.3). 



M 











Pi 


p-value 


= 0.09 












-s 


1 


































p 
















ft 


i- 




m 






















• 


i> 


f' 









Figure 4.3. Example of an approximate EPDF. Histogram represents the distribution of 
100 outcomes obtained by Monte Carlo simulation. A subsequent observation, jj'*, is 
represented by the vertical line and the approximate tail-area probability is 0.09. 



4.1.7. Details of the Iterative Approach 

An iterative process is used to calibrate the simulation model (Fig. 4.4). Initial 
movement algorithms and parameter values are selected for the first experiment. Once the 
experimental design is selected and the simulation runs are completed, bum-in time is 
evaluated for each summary outcome for each EU. Experiment bum-in time is estimated 
as the maximum bum-in time of all evaluated summary outcomes for all EUs. Statistical 
analyses are performed on each discrepancy measure from the time interval (i.e., annual 
cycle) following estimated experiment bum-in time. Based on the results of these 
analyses and subjective opinions from viewing simulation output, settings for the next 
simulation experiment are determined. Movement algorithms are changed or parameter 
values are adjusted, as appropriate, in subsequent experiments. When the discrepancy 
measures appear to be minimized, multiple runs of the simulation with the same 



52 



parameter values are conducted and the distributions of the simulated summary statistics, 
relative to the observed summary statistics, are evaluated using predictive p-values. 



Estimate algorithms and parameter values 





Getting closer to 
the optimum? 




Design and conduct 
simulation experiment 



Determine bum-in time for experiment 



Analyze simulated data 




>{ Calibration complete 



Figure 4.4. Flow chart representing the iterative process of model calibration. 



53 
4.2. Initial Model Parameterization 

This first series of calibration experiments focused on parameterization of the 
adult female movement process. Once female movements were sufficiently calibrated, the 
algorithms and parameters were adjusted for calibration of the male movement process. 

In the movement process that was developed, each deer made multiple moves per 
day. In order to make valid comparisons of the simulated data and the observed field data, 
only some locations of the simulated deer (i.e., one radio-location every 5 days) were 
used for calculation of the outcome summary statistics. These statistics included home 
range size, distance between consecutive annual home range centers, distance between 
two consecutive radio-locations (5 days apart), and percentage of observations in each 
habitat. 

Initial locations of simulated deer were representative of home range centers of 
observed deer fi-om the calibration data set. The habitat map over which deer moved was 
a closed environment (i.e., deer could not move off the map); however, there was no 
'repelling force' to prevent them fi-om moving to the edge of the map. Simulated deer that 
moved adjacent to tiie map boundary had fewer pixels from which to choose for their next 
location since there was a zero probability of moving to a pixel not within the study area. 
These deer that formed home ranges on the boundary of the habitat map may not have 
had realistic movement patterns; therefore, tiiey were removed from data analyses for 
model calibration. 

4.2.1. Movement Step Size 

The habitat map was created using 20-m pixels; however, there were several 
problems simulating deer movements on a scale that small. Simulated deer that moved a 



54 

maximum distance of one pixel per step (to one of the eight neighboring pixels or to the 

current location) had to make a very large number of steps to cover a suflFicient portion of 
its home range over a 5-day period. Also, simulated deer were stranded in large regions of 
continuous habitat (e.g., large areas of prairie) and wandered randomly, never finding 
other habitats. Although some observed deer spent nearly all their time in the prairie, a 
high proportion of the deer in early simulations exhibited this behavior. One alternative 
possibility was to allow deer to move farther than one pixel per step. Although deer 
traveled longer distances during one day, they would 'jump' from one location to another, 
leaving 'holes' in the memory of its previous locations. These simulated deer tended to 
wander over the entire landscape, probably because home range formation is partly based 
on an algorithm using memory of previous locations. 

To address this problem, a single iteration of simulated deer movement was 
developed as a two-stage process. First, deer selected a new location, using pixels larger 
than 20-m, and then selected a 20-m pixel within the large pixel. Because the dynamics of 
the simulated movements changed drastically as the size of the large pixel changed, 
evaluation of the potential pixel sizes quantitatively would require developing an 
optimum set of parameters for each pixel size and then comparing the optimized models. 
This approach was not feasible given the amount of computer time needed to optimize a 
single simulation model. Thus, the size of the large pixel was chosen to be 60-m for 
several more qualitative reasons. An average home range of 300 ha contained 
approximately 7500 20-m pixels, 1875 40-m pixels, 833 60-m pixels, 469 80-m pixels, 
300 100-m pixels, or 20 500-m pixels. Small pixel sizes required deer to make a large 
number of movements to cover most of the home range during a reasonable time interval. 



Large pixel sizes required fewer movements to cover most or all of the home range; 
however, these large pixels also drastically reduced the resolution of the habitat map. Use 
of a lower resolution when developing the habitat map would have caused the loss of 
many of the small tree islands and other small features of the landscape (K. E. Miller, 
personal communication). If the large pixels used in the simulation model were 'too 
large', simulated deer were less likely to find and utilize the smaller habitat features. A 
compromise between the two extreme scenarios was to develop the simulation with 60-m 
large pixels, each containing nine 20-m small pixels (Fig. 4.5). 

In summary, simulated deer made multiple movements over a 5-day interval, the 
interval over which simulated 'radio-locations' were taken. In the first stage of each 
movement iteration, using 60-m pixels, deer moved a maximum distance of one pixel in 



-- 60 m - 








♦ 








/ 
















.• 












1 1 






r 











Figure 4.5. Two-stage movement process of a simulated deer using large 60-m pixels. 
The hypothetical deer moved from the upper left 20-m pixel in the center 60-m pixel to 
the lower right 20-m pixel in the lower left 60-m pixel. 



S6 

any direction. During this stage, a deer evaluated its surroundings and determined the 
probabihty of moving to each pixel based on habitat, water depth, and relative location in 
its home range. The second stage consisted of selecting a 20-m pixel, based on habitat 
and water depth, within the 60-m pixel. 
4.2.2. 60-in Movement Stage 

hi the first stage of a movement step, each deer evaluated its surroundings based 
on habitat, water depth, and relative location in its home range. A relative affinity score, a 
continuous, ratio variable, was assigned to each pixel for each factor. For example, if a 
deer had to choose between two pixels, with relative affinity scores of 5 and 10, it would 
be twice as likely to move to the pixel with a relative affinity of 10 than it would be to 
move to the pixel with a relative affinity of 5. These scores were converted to 
probabilities of moving to given pixels and averaged, using methods detailed below. Final 
values for the relative affinity scores for each factor were determined during the 
calibration process. 
4.2.2.a. Habitat 

Each 20-m pixel was assigned a relative affinity score based on habitat contained 
inside the pixel. Initial values for the relative affinities (Table 4.1) were updated 
throughout the calibration process. Relative affinity scores for the 60-m pixels were 
determined using the mean relative affinity of the nine 20-m pixels it contained. The 
mean relative affinity score for each 60-m pixel was standardized by converting it to a 
probability: 












S7 


affinity J 








yj- 9 








Zj affinity J , 




* ' ' '■ 




y=i 


■/ '- 







fory" = 1, 2, 3, . . . , 9 and where/?, was the probability of moving to pixely based solely on 
habitat, and affinity ^ was the relative affinity score for pixely. For example, if the nine 60- 
m pixels to which a simulated deer could move had relative affmity scores for habitat of 
20, 30, 40, 10, 10, 50, 50, 20, and 30, then the probability of moving to each pixel based 
on habitat would be 0.08, 0.1 1, 0.15, 0.04, 0.04, 0.19, 0.19, 0.08, and 0. 11, respectively. 

Table 4.1. Initial habitat relative affinity scores. 



Habitat 


Symbol 


Relative affmity 


Wet prairie 


^WPR 


10 


Herbaceous prairie 


^HPR 


20 


Tree island 


A^TRE 


50 


Willow/dense sawgrass 


^WSA 


50 


Cypress prairie/strand 


^YS 


10 


Pine 


^PIN 


10 


Mangrove 




1 



4.2.2.b. Water depth 

Water depth in each 20-m pixel was calculated from the water depth at P-34 
(centrally located water gauge) and the relative elevations of each habitat (Section 2.2.2). 
For model calibration, an aimual water depth cycle was repeated for each year of the 
simulation. This annual cycle was based on the average monthly water depth at P-34 
during the collection of model calibration data (Table 4.2). 

Water depth in each 60-m pixel was calculated as the mean depth of water in the 
nine 20-m pixels it contained. A relative affinity score for each pixel was calculated as 



58 



affinity J = ■ 



a 



a- 



a- 1 



(depth - p) 



if depth < p 

\ip< depth < y 
if depth > y 



foTj = 1, 2, 3, . . . , 9 and where a, P, and y were the parameters with values determined 
during the calibration process (Fig. 4.6). The relative affinity for each pixel was 
standardized by converting it to a probability: 

affinity J \ -: •..,»■'• , 

Pj = -9 

Zi affi"fO'j ■'' ''m,' ; 

fory = 1, 2, 3, . . . , 9 and where ;?^ was the probability of moving to pixely based solely on 
water depth, and affinity j was the relative affinity score for pixel y. 



Table 4.2. Monthly water depths at P-34 for one annual cycle of the calibration 
simulation, using average water depths for each month from April 1989 to Mar ch 1992. 
Month Depth (cm) Month Depth (cm) 



April 


-40.78 


October 


20.56 


May 


-30.00 


November 


10.81 


June 


-0.06 


December 


-1.50 


July 


19.79 


January 


-9.42 


August 


27.99 


February 


-16.39 


September 


28.51 


March 


-27.10 



59 









affinity 




' " ' . ■-' 




.1 

(0 

0) 

on 

1 0- 


1 


\ 




I i 



P Y 

Water depth 



Figure 4.6. Relationship between water depth and relative affinity for moving to a 
particular pixel, with the minimum affinity score set at 1 . a, p, and y were parameters 
optimized in the model calibration. 



4.2.2.C. Home range 

Two algorithms utilizing the previous locations of a deer induce the formation and 
maintenance of home ranges. A homing beacon encouraged movement towards the center 
of the home range, and pixel memory encouraged deer to move to pixels visited in their 
recent past (e.g., 2 months). A combination of the two algorithms was utilized because 
neither performed adequately when used alone. The homing beacon produced circular 
home ranges with little variation in size, and the pixel memory algorithm was not strong 
enough to maintain the strong site fidelity of these deer. However, together these 
algorithms produced home ranges that varied in shape and size and that maintained a 
realistic degree of site fidelity in the simulated deer. 

The homing beacon algorithm provided simulated deer with a stronger affinity for 
pixels closer to their homing beacon, (x^„^^ , >7^^^^ ) , than away from their homing 



60 

beacon. The location of the homing beacon, based on A: previous radio-location 
coordinates (one taken every 5 days), was updated every 5 days using the moving 
averages: 

yhomc = j(y, + y,-i + yi-2+-+y,-k+\) 

where (x,, y,) were the coordinates of the most recent radio-location and (x,_^, y,_{) were the 
coordinates of the radio-location taken 5 days earlier, etc. The window of time used to 
calculate the location of the homing beacon encompassed the ^ prior radio-locations. 

The relative affinity scores for the nine 60-m pixels to which the deer could move 
were based on the direction of travel from the current location of the individual deer to 
the homing beacon (Fig. 4.7). To avoid simulated deer from gradually shrinking their 
home ranges due to a concentration of movements around the homing beacon, the 
strength of the beacon, 6 (equal to 1, -^ , or cj)), was reduced exponentially as a deer 
moved closer to its beacon: 



affinity J = • 



z/ 

S^^ if z < ju 
S otherwise 



fory = 1, 2 ,3, . . . , 9, and where S or S''^'' was the relative affinity score, \i was the 
distance from the homing beacon at which relative affinity was constant, and z was the 
distance from the current location to the homing beacon. The final values for ^ (>0) and 
]i (>0) were estimated through model calibration; in initial simulations, (J)=3 and |i=750 



m. 



61 



(a) 








(b) 








(c) 








1 


1 


1 




1 


(l> 


<t> 




1 


1+ 4> 

2 


1+0 

2 


N 


4> 


<t> 


(t> 


1 





<t> 


2 








>k 


(t> 


<t> 


(P 


1 


(P 


<t> 


2 





<t> 



Figure 4.7. Illustration of relative affinity calculations for the homing beacon, with the 
homing beacon located southeast of the current location [center pixel of (a), (b), and (c)]. 
Affinity scores to move (a) towards the south and (b) towards the east were averaged to 
give (c) 6 (equal to 1, i±^ , or cj)) which was used to calculate the relative affinity scores of 
moving to each of the nine possible pixels. 



The pixel memory algorithm provided simulated deer with a stronger affinity for 
previously visited pixels than for those not visited in the recent past. The relative affinity 
score for pixel y was defined as 



affinityj 



X if pixel j visited during known memory 
1 otherwise 



fory = 1, 2, 3, . . . , 9 and where A. (>1) was the relative affinity. Each simulated deer had 
a map of its recent locations created with a moving window, containing all previous 
locations of a deer for a given period of time (e.g., 2 months). This map was used to 
assign relative affinity scores for each of the nine 60-m pixels a deer evaluated for each 
step. The final value for A, was estimated through model calibration; in the initial 
simulations, X=A. 



62 

The relative affinity scores for the homing beacon algorithm and for the pixel 
memory algorithm for each of the nine 60-m pixels were standardized by converting them 
to probabilities: ^ . 









Z affinity . ,* , .- r . -, 



fory = 1, 2, 3, . . . , 9 and where p^ was the probability of moving to pixely and affinity j 
was the relative affinity score for pixel y either for homing beacon or for pixel memory. 
4.2.2.d. Combining movement factors 

The probability of moving to each of the nine 60-m pixels was calculated, for each 
of the four algorithms as described above. For each pixel, the probabilities for each factor 
were averaged to give the probability of moving to each pixel: 

fory = 1, 2, 3, . . . , 9 and where /7,y,/72y,/>3y, andp^j were probabilities of moving to pixel 
j based on habitat, water depth, homing beacon, and pixel memory, respectively. The deer 
chose a 60-m pixel for its next location based on a random draw fi-om the multinomial 
distribution (ti,, -nij) T^i, ■ ■ ■ , ^19). 
4.2.3. 20-m Movement Stage 

The nine 20-m pixels contained inside the 60-m pixel of the location of the deer 
were evaluated based on habitat and water depth. Relative affinity scores were used to 
calculate the probabilities of moving to each 20-m pixel based habitat and based on water 
depth. These probabilities were averaged to obtain the probability of moving to each of 



the nine 20-m pixels: 



^J-^(ph'P2j) 



forj = 1, 2, 3, . . . , 9 and where/? \j andp y were the probabilities of moving to the 20-m 
pixel; based on habitat and water depth, respectively. The deer selected a 20-m pixel 
based on a random draw from the multinomial distribution (t:',, n'j, n'j, . . . , 71: '5). 
4.2.4. Simulation Initialization 

The simulation began with 30 deer in a set of specified locations that were 
representative of the home range centers of the deer included in the calibration data set. 
Each deer started the simulation with no history or memory of previous locations. During 
the time deer were building their initial memory map and homing beacon coordinates, 
their movements were a function of habitat and water depth only. Once the simulation ran 
for the length of the memory of a deer (e.g., 2 months), a deer began to use the home 
range algorithms in its movement steps. 

4.3. Model Calibration Experiments 
In this section, the fu-st two of a series of calibration experiments for females were 
discussed. In these two experiments, only annual summary outcomes were evaluated; 
however, data from later experiments were analyzed to explore and calibrate seasonal 
patterns. These two experiments and subsequent experiments for females were described 
m Appendix C, and calibration experiments for males were discussed in Appendix D. 



64 
4.3.1. First Calibration Experiment 

The first experiment focused on the number of two-stage movement steps over a 
5-day interval and parameter values for the home range algorithms (Table 4.3). A one- 
half fraction of a 2* factorial design (i.e., 2*' fi-actional factorial) was used. This design 
allowed estimation of all main effects and first-order interactions with 10 degrees of 
freedom for experimental error, assuming higher-order interactions were negligible. Each 
of the 32 EUs consisted of 30 deer with same starting coordinates, located in areas where 
the majority of the study deer had resided. 

Table 4.3. Factor levels for the first calibration experiment. 

Factor description Symbol Low High 

Maximum affinity for homing beacon 

Distance (m) from homing beacon at which 
affinity is cj) 

Relative affinity for previously visited pixels 

Memory length (5-day intervals) 

Number of steps per 5-day interval 

Relative affinity score for tree islands and 
willow/dense sawgrass 

The movement algorithms in this experiment were those discussed in Section 4.2 
with the exception of water depth. Since simulation bum-in time may have been 
confounded with temporal effects of water levels, seasonally fluctuating parameters and 
algorithms were not included. After several experiments were completed and a reference 
value for bum-in time was estimated, water depth was included as a factor in the 
simulation experiments (Table C.6). Until water depth was included in the model, the 
probability of moving to each large-scale pixel was calculated as 



4> 


3 


5 


\i 


750 


1750 


X 


4 


12 


ML 


12 


36 


STEP 


100 


300 


"^TRE.WSA 


30 


SO 



65 
1 1 1 

fory = 1, 2, 3, . . . , 9 and where p^J,p2J, andp^j were the probabilities of moving to pixel 
j based on habitat, homing beacon, and location memory, respectively. 

Simulations were run for an extended period of time to adequately estimate bum- 
in time. At this stage of calibration of the simulation model, the main focus was to 
simulate movement patterns of deer and understand the temporal and spatial dynamics of 
the movement algorithms. Although longer than the expected life span of a white-tailed 
deer, each EU was run for 15 years. Based on preliminary simulations, a simulation 
length of 15 years was sufficient to determine if and when a steady-state had been reached 
by the outcome measures (e.g., annual home range size and percentage of observations in 
each habitat). Incorporating additional dynamics, such as recruitment and mortality, 
would make the simulation more realistic, but adequate evaluation of the dynamics of the 
movement algorithms would be difficult because of the potential for confounding. 
Additionally, only 1 year of data (the year following experiment bum-in) from of each EU 
was used for analysis of the factorial experiment, thus minimizing the effect of population 
dynamics examined simulation outcomes. 

For the simulated data to be comparable to observed data, 72 locations per year (1 
per 5 days) were used to calculate outcome measures. Annual home range size, distance 
between consecutive annual centers of activity, mean distance between consecutive 
locations, and percentage of observations in each habitat were calculated and used as 
outcome statistics. 






■ ■ ' ' ' - 66 

A series of repeated measures ANOVAs was performed on the annual outcome 
measures to estimate bum-in time. A separate analysis for each outcome for each of the 
32 EUs was performed. These outcomes were annual home range size, distance between 
consecutive annual centers of activity, mean distance between consecutive locations, and 
percentage of radio-locations in each of the four major habitats in the study area (i.e., wet 
prairie, herbaceous prairie, tree islands, and willow/dense sawgrass). Several covariance 
structures were evaluated before testing specific hypotheses regarding temporal trends. 
Compoimd symmetry assumed equal correlation among all years. An auto-correlation 
structure assumed correlation among years was a fimction of "distance" between any pair 
of years (i.e., the correlation between outcomes from year / and yeary was equal to p'''^'). A 
heterogenous auto-correlation structure was similar to an auto-correlation structure, with 
additional parameters to estimate variances for each year. Akaike Information Criterion 
values (AICs), log-likelihood values penalized for the number of estimated parameters 
(Akaike 1974), were compared to determine the most appropriate structure for each 
outcome measure. For distance between consecutive annual centers of activity, mean 
distance between consecutive locations, and percentage of radio-locations in each of the 
four major habitats, the auto-correlation structure provided the best fit. For annual home 
range size, the heterogenous auto-correlation structure provided the best fit. Tests for 
linear time trends were used to estimate bum-in time for each EU for each outcome. 
Based on an a-level of 0.01, the maximum bum-in time was estimated at 4 years, so 
summary data from the S"" year of simulation were used to evaluate the adequacy of the 
simulation model parameters (Tables 4.4 and 4.5). Data from the 6* year to the IS"" year 
of the simulations were not used in the following analyses. 



67 



Table 4.4. Summary outcome measures of home range size, distance between 
consecutive home range centers, and distance between consecutive locations from first 
calibration experiment for adult females from the 5"* year of simulation. 



d) ^ A ML STEP A,^^3, Homerange Ammal center 5-day 

TREwsA size (ha) shift (m) distance (m) 



3 750 


4 


12 


100 


30 


563 


1134 


486 


3 750 


4 


12 


300 


50 


709 I 


i 1181 


737 


3 750 


4 


36 


100 


50 


502 


703 


503 


3 750 


4 


36 


300 


30 


815 ^ 


453 


800 


3 750 


12 


12 


100 


50 


436 


913 


458 


3 750 


12 


12 


300 


30 


734 


920 


738 


3 750 


12 


36 


100 


30 


543 


1118 


465 


3 750 


12 


36 


300 


50 


539 


681 


685 


3 1750 


4 


12 


100 


50 


792 


1460 


499 


3 1750 


4 


12 


300 


30 


1426 


1523 


830 


3 1750 


4 


36 


100 


30 


715 


862 


524 


3 1750 


4 


36 


300 


50 


1044 


588 


842 


3 1750 


12 


12 


100 


30 


698 


1411 


482 


3 1750 


12 


12 


300 


50 


953 


1292 


741 


3 1750 


12 


36 


100 


50 


638 


1381 


470 


3 1750 


12 


36 


300 


30 


1058 


1318 


776 


5 750 


4 


12 


100 


50 


428 


538 


496 


5 750 


4 


12 


300 


30 


568 


351 


747 


5 750 


4 


36 


100 


30 


474 


646 


509 


5 750 


4 


36 


300 


50 


538 


372 


734 


5 750 


12 


12 


100 


30 


397 


432 


499 


5 750 


12 


12 


300 


50 


474 


362 


734 


5 750 


12 


36 


100 


50 


356 


424 


4tl 


5 750 


12 


36 


300 


30 


519 


337 


721 


5 1750 


4 


12 


100 


30 


662 


625 


saa 


5 1750 


4 


12 


300 


50 


831 


565 


m 


5 1750 


4 


36 


100 


50 


528 


746 


m 


5 1750 


4 


36 


300 


30 


951 


504 


847 


5 1750 


12 


12 


100 


50 


487 


710 


487 


5 1750 


12 


12 


300 


30 


908 


568 


81f 


5 1750 


12 


36 


100 


30 


556 


589 


502 


5 1750 


12 


36 


300 


50 


785 


536 


790 



68 

Table 4.5. Summary outcome measures of percentage of radio-locations in each habitat* 
from first calibration experiment for aduh females from the S"* year of simulation. 

.„ ^^^x. . Percentage of radio-locations in each habitat 

<p 11 A ML STEP AxRFwsA 

^"^■^^^ WPR HPR TRE WSA CYP MAN 



3 


750 


4 


12 


100 


30 


37.2 


33.0 


14.5 


3.3 


5.0 


0.6 


3 


750 


4 


12 


300 


50 


32.7 


23.2 


26.5 


4.8 


4.4 


0.0 


3 


750 


4 


36 


100 


50 


43.0 


17.3 


24.2 


4.2 


1.7 


0.2 


3 


750 


4 


36 


300 


30 


40.3 


27.5 


21.9 


3.4 


0.9 


0.0 


3 


750 


12 


12 


100 


50 


28.1 


24.6 


32.0 


4.6 


1.5 


0.1 


3 


750 


12 


12 


300 


30 


31.1 


30.2 


23.8 


4.1 


3.3 


0.0 


3 


750 


12 


36 


100 


30 


43.5 


22.9 


19.0 


2.1 


5.0 


0.2 


3 


750 


12 


36 


300 


50 


24.3 


24.2 


33.7 


5.8 


2.3 


0.1 


3 


1750 


4 


12 


100 


50 


36.9 


18.1 


26.2 


4.0 


6.3 


1.0 


3 


1750 


4 


12 


300 


30 


34.1 


33.1 


16.6 


3.1 


4.7 


0.1 


3 


1750 


4 


36 


100 


30 


48.2 


21.6 


16.1 


3.1 


1.3 


0.0 


3 


1750 


4 


36 


300 


50 


29.3 


29.8 


24.9 


4.6 


3.7 


0.0 


3 


1750 


12 


12 


100 


30 


38.0 


28.4 


17.4 


3.1 


5.6 


0.2 


3 


1750 


12 


12 


300 


50 


23.3 


28.2 


34.2 


5.0 


1.1 


0.1 


3 


1750 


12 


36 


100 


50 


41.5 


16.5 


20.1 


4.1 


6.3 


0.7 


3 


1750 


12 


36 


300 


30 


38.3 


26.9 


19.5 


3.8 


4.7 


0.0 


5 


750 


4 


12 


100 


50 


30.3 


28.6 


23.6 


3.7 


4.1 


0.9 


5 


750 


4 


12 


300 


30 


43.1 


31.2 


16.9 


2.6 


0.8 


0.0 


5 


750 


4 


36 


100 


30 


46.7 


28.5 


15.4 


2.8 


0.5 


0.0 


5 


750 


4 


36 


300 


50 


31.9 


21.6 


27.5 


5.3 


0.9 


0.0 


5 


750 


12 


12 


100 


30 


42.6 


28.4 


16.5 


2.6 


3.1 


0.2 


5 


750 


12 


12 


300 


50 


33.6 


21.9 


28.3 


4.8 


1.9 


0.0 


5 


750 


12 


36 


100 


50 


45.0 


14.4 


25.3 


5.3 


1.7 


0.1 


5 


750 


12 


36 


300 


30 


30.2 


31.5 


28.5 


3.0 


1.4 


0.3 


5 


1750 


4 


12 


100 


30 


43.5 


31.3 


15.9 


2.1 


1.4 


0.1 


5 


1750 


4 


12 


300 


50 


34.1 


20.6 


29.2 


5.3 


2.4 


0.2 


5 


1750 


4 


36 


100 


50 


30.4 


22.9 


25.3 


4.7 


5.2 


0.0 


5 


1750 


4 


36 


300 


30 


41.1 


26.8 


20.0 


3.8 


1.2 


0.0 


5 


1750 


12 


12 


100 


50 


31.8 


22.0 


27.1 


5.7 


1.7 


0.0 


5 


1750 


12 


12 


300 


30 


37.3 


36.2 


17.0 


2.9 


0.6 


0.2 


5 


1750 


12 


36 


100 


30 


41.8 


25.4 


18.1 


4.6 


2.9 


0.0 


5 


1750 


12 


36 


300 


50 


31.1 


24.6 


28.0 


4.2 


3.3 


0.2 



" WPR=wet prairie, HPR=herbaceous prairie, TRE=tree island, WSA=willow/dense 
sawgrass, CYP=cypress/pine, MAN=mangrove/mangrove-prairie transition. 



m 

For each of the summary outcome measures of amiual home range size, distance 
between annual centers of activity, and distance between consecutive radio-locations, a 
discrepancy measure (DM) was calculated. First, for each EU, the mean outcome measure 
was calculated (e.g., mean home range size for 30 deer in the 6* year of the simulation for 
the /* EU). Then, for each EU and for each summary outcome, the DM was calculated as 

for / = 1, 2, 3, . . . , 32 and where O was the observed summary outcome and P/x) was the 
summary outcome from the /"" EU based on the simulation model. On an annual basis, the 
observed summary statistics for females were mean home range size of 271 ha, mean 
distance between consecutive centers of 307 m, and mean distance between consecutive 
locations of 686 m (Section 3.3.1). 

For the summary outcome measures of percentage of observations in each habitat, 
a discrepancy measure (DM) also was calculated. First, for each EU, the mean outcome 
measure was calculated (e.g., mean percentage of observations in wet prairie for 30 deer 
in the 6"' year of the simulation for the f^ EU). The DM for habitat use was calculated for 
the /•* EU as 



z>,w=i^''*''-"')^ 



y=i O 



J 



for / = 1, 2, 3, . . . , 32 and where O, was the mean percentage of time observed deer were 
radio-located in habitaty and P/x) was the mean percentage of time simulated deer were 
located in habitaty. On an annual basis, the observed summary statistics for females 



were 



70 

50%, 17%, 17%, 9%, 2%, and 2% of radio-locations in wet prairie, herbaceous prairie, 

tree islands, willow/dense sawgrass, cypress/pine, and mangrove, respectively (Section 
3.3.1). 

An ANOVA to test for main effects and first-order interactions of the evaluated 
simulation parameters vi'as performed for each of the four DMs (Table 4.6). Statistical 
significance was determined using an a-level of 0.05; however, effect size (i.e., relative 
decrease in the DMs) also was taken into account when determining the most influential 
factors and the levels to be used in the subsequent simulation experiment. 

All average home range sizes of the simulated females were larger than those of 
females observed in the field. The DM for home range size was significantly smaller with 
smaller (j), smaller [i, larger X, smaller STEP, and larger Atre.wsa (see Table 4.3 for factor 
descriptions). Distance between consecutive annual centers ranged from very close to the 
observed average to more than three times the observed average. The DM for distance 
between consecutive centers was reduced with larger (j), smaller [i, and a longer ML. 

Average distance between consecutive locations ranged from 458 m to 847 m, 
encompassing the observed value of 686 m. The DM for mean distance between 
consecutive locations was significantly smaller with smaller \i and larger STEP. Also, 
there were significant interactions between X and STEP and between Atre^sa and STEP. 
The interaction between X and STEP indicated that when STEP=100, an increase in X 
caused an increase in the DM and when STEP=300, an increase in X caused a decrease in 
the DM. The interaction between Atre,wsa and STEP indicated that when STEP=100, an 
mcrease in At.re,wsa caused an increase in the DM, and when STEP=300, an increase in 
Atre.wsa caused a decrease in the DM. 



;>-.v^^o^ 



71 



Table 4.6. Summary of ANOVA results (p-values) from the first calibration experiment 
for each DM from the 5"' year of simulation. 

„ .T- . Home Annual 5-day ,, , . ^ 

Expenment Factor ... .. ■' Habitat use 

. range size center shift distance 



^ 


0.0001 


0.0001 


0.6471 


0.2707 


V 


0.0001 


0.0030 


0.0013 


0.8645 


X 


0.0020 


0.5000 


0.1600 


0.2588 


ML 


0.1853 


0.0277 


0.8252 


0.0475 


STEP 


0.0001 


0.0708 


0.0001 


0.0279 


■^TRE.WSA 


0.0014 


0.7571 


0.4403 


0.4109 


<t>*li 


0.1642 


0.2315 


0.1686 


0.9795 


(\>*X 


0.2139 


0.1823 


0.4383 


0.3754 


\i*X 


0.4672 


0.3137 


0.6073 


0.7999 


(t)*ML 


0.2764 


0.0274 


0.8643 


0.2044 


ti*ML 


0.2264 


0.6255 


0.5227 


0.4663 


A* ML 


0.3905 


0.0568 


0.3659 


0.9218 


<j) * STEP 


0.0739 


0.9324 


0.1663 


0.5359 


\i * STEP 


0.0008 


0.7396 


0.0001 


0.6528 


X * STEP 


0.3346 


0.8458 


0.0005 


0.1028 


ML * STEP 


0.5827 


0.2778 


0.7040 


0.2202 


V A-TRE wSA 


0.3688 


0.5001 


0.2724 


0.3010 


M' AjR£^sA 


0.4406 


0.9300 


0.3113 


0.3871 


1 * A 

'^ ^TRE.WSA 


0.8761 


0.6816 


0.7797 


0.8811 


MT * A 

ivil^ ^TRE.WSA 


0.6918 


0.6783 


0.9174 


0.4974 


CXPP * A 


0.0905 


0.6761 


0.0217 


0.9590 



Habitat use patterns of the simulated female deer (Table 4.5) were not comparable 
to those of the observed female deer (Table 3.2). Simulated females were observed in tree 
islands and herbaceous prairie more and wet prairie less than observed females, indicating 
a need for further evaluation of relative habitat affinities. An increase in ML and a 
decrease in STEP caused a decrease in the DM for habitat use. Atre,wsa and its associated 
interactions had no significant effect on the DM, perhaps because the overall agreement 
was poor. 



72 

In addition to quantitative analyses of simulation results, qualitative observations 
also aided in the verification and calibration processes. Movement paths of simulated and 
observed female deer residing in the same area on the landscape were plotted and 
compared. For example, during a 1-year interval, one simulated deer had a realistic 
movement pattern when compared to an observed deer (3-year-old female) in the same 
geographic area; however, the movement paths of all simulated deer were not similarly 
realistic, indicating the model still needed improvement (Fig. 4.8). 

The outcome measures that had the greatest disagreement with the observed 
summary data were home range size and habitat use. Analysis results for each summary 
outcome indicated a direction in the parameter space to move in order to minimize the 
DM; however, these directions were contradictory for several of the DMs. So, for the 
subsequent experiment, current parameter settings were maintained. Instead, I focused on 
minimizing the habitat use discrepancies by including additional factors (e.g., relative 
affinities for herbaceous prairie, willow/dense sawgrass, cypress, pine, and mangrove) in 
the following experiment. 
4.3.2. Second Calibration Experiment 

The second experiment focused on the number of steps over a 5-day interval, 
parameter values for the home range algorithms, and values for relative habitat affinities 
(Table 4.7). A 2"'* fractional factorial design was used, which allowed estimation of all 
main effects with 20 degrees of freedom for experimental error, assuming interactions 
were negligible. As in the first experiment, each of the 32 EUs consisted of 30 deer, 
starting in the same locations, simulated for a 1 5-year time interval. The movement 
algorithms were not changed from those used in the first calibration experiment. 



73 







-^ ■ , ^^^>'-^' 



,^ 



(a) -^ 




;^'4»km 



■^.?^',^^. 



:^-: 



^^«^vy 






• #i>'^ 








^ 


^ 


*._ 


t 


< iB' 




r-- - ' 


. ,^ /•'..- 


,;^J 




'J^^\^ . 


n 


„ -f 


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^ 


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.. »' 






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.,\^ 


v^ 


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<'^T 


\ 


"/<■ 


^'■■^ 


. #^ 











'0* • • -■■--, 



^'^ ^-^'^Tfi^ /T ^^^ ^-^ -^ 




^-.^a^sfci^ 



Wet Prairie 



Tree island 



I I Herbaceous Prairie 1"^ Willow/dense sawgrass 



Figure 4.8. Examples of observed and simulated deer movement paths over a 1-year time 
period, (a) observed adult female; (b) observed adult female; (c) simulated female 
exhibiting a movement path comparable to the observed females; and (d) simulated 
female not exhibiting typical site fidelity of observed females. 



74 



Table 4.7. Factor levels for second calibration experiment. 



* 


3 


5 


^ 


750 


1750 


X 


4 


12 


ML 


12 


36 


STEP 


100 


300 


■^HPR 


20 


30 


-'^TRE 


20 


50 


■^WSA 


30 


50 


■^YS 


5 


15 


^PIN 


5 


15 


Aman 


1 


10 



Factor description Symbol Low High 

Maximum relative affinity for homing beacon 

Distance (m) from homing beacon at which 

affinity is ^ 
Relative affinity for previously visited pixels 
Memory length (5-day interval) 
Number of moves per 5 -day interval 
Relative affinity for herbaceous prairie 
Relative affinity for tree islands 
Relative affinity for willow/dense sawgrass 
Relative affinity for cypress 
Relative affinity for pine 
Relative affinity for mangrove 

Annual home range size, distance between consecutive annual centers of activity, 
mean distance between consecutive locations, and percentage of observations in each 
habitat were the calculated outcome measures. Using the outcome measures for each of 
the 15 years of simulation, repeated measures ANOVA was conducted to estimate bum-in 
time, with a separate analysis for each outcome for each of the 32 EUs. Correlation 
structures providing the best fit to the data for each outcome were the same as in the first 
experiment. For distance between consecutive annual centers of activity, mean distance 
between consecutive locations, and percentage of radio-locations in each of the four 
major habitats, the auto-correlation structure provided the best fit. For aimual home range 
size, the heterogenous auto-correlation structure provided the best fit. Tests for linear 
time trends were used to estimate bum-in time for each EU for each outcome. Based on 
an a-level of 0.01, the maximum bum-in time was estimated at 5 years; thus, summary 



75 

data from the 6* year of simulation were used to evaluate the adequacy of the simulation 

model parameters (Tables 4.8 and 4.9). 

DMs were calculated for annual home range size, distance between consecutive ? 
radio-locations, distance between annual centers, and habitat use for each of the 32 EUs 
as in the first experiment. In addition to the four DMs, a mean discrepancy (MD) for each 
EU was also calculated: 



1 
MD= - 

4 



(d -D "^ ^- - ^ 



'HR ^HR 



S 



DsD - D,o 



s 



(d -D ] (d -D ^ 



HR ^ \ ^5D ^ V 'JQS J V '^Hu 



Sr 



s. 



where D^^, /)„, I>5o, and D^^^J were the discrepancies for home range, annual center shift, 
5-day distance, and habitat use (Table 4.9). D„^ , D^^ , D^j^ , and D„y were the mean 
discrepancies and S„g, 5„, S;^, and Sfj^ were the standard deviations for home range, 
annual center shift, 5-day distance, and habitat use discrepancies for this experiment. This 
measure provided an indication of the factors evaluated in the experiment that had the 
greatest effect on lack-of-fit of the simulation model output when averaging over all 
DMs. 

An ANOVA testing for main effects of the evaluated simulation parameters was 
performed for the each of the four DMs and MD using a significance level of 0.05 (Table 
4.10). The DM for home range size was significantly smaller with smaller ^, smaller \i, 
larger A, smaller STEP, and larger Atre (see Table 4.7 for factor descriptions). The DM 
for distance between consecutive annual centers was reduced with larger (J), smaller [i, 
longer ML, and larger STEP. The DM for mean distance between consecutive radio- 
locations was significantly smaller with larger STEP. The DM for habitat use was 



76 



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80 

significantly smaller with smaller Ahpr. Overall, habitat use of the simulated deer 

exhibited strong lack of fit evidenced by the large values of the chi-square DM and the 
mean percentage of observations of simulated deer in each habitat. Adjustments to 
relative affinity scores for the subsequent experiment were made based on the mean 
percentage of radio-locations in each habitat for each of the relative affinities (Table 

4.11). ^^:} ' • ^ ,r ■ t%r -C 



Table 4.10. Summary of ANOVA results (p-values) fi-om the second calibration 

experiment for each DM and the mean discrepancy for the 6"' year of simulation. 

Experiment Home range Annual 5 -day Mean 

Factor size center shift distance Habitat use discrepancy 



* 


0.0001 


0.0001 


0.3439 


0.4387 


0.0001 


\^ 


0.0001 


0.0001 


0.1761 


0.1647 


0.0001 


X 


0.0024 


0.1313 


0.7828 


0.6787 


0.1625 


ML 


0.6581 


0.0001 


0.4619 


0.6956 


0.0005 


STEP 


0.0001 


0.0001 


0.0001 


0.0367 


0.3152 


■'^HPR 


0.6133 


0.0504 


0.5917 


0.0029 


0.1293 


Atre 


0.0309 


0.0448 


0.9891 


0.1876 


0.0238 


■^WSA 


0.7129 


0.1430 


0.8878 


0.0661 


0.2955 


-^CYS 


0.7703 


0.7923 


0.5421 


0.7149 


0.9397 


■''^PIN 


0.8733 


0.7072 


0.8288 


0.6987 


0.5496 




0.6354 


0.6388 


0.7003 


0.8825 


0.9921 



MD was significantly reduced with larger (j), smaller [i, and longer ML. MD was 
also reduced with larger Aj^. This finding was misleading because with larger A^re, 
home range sizes had smaller discrepancies; however, concurrently, the percentage of 
locations of individuals in tree islands was much higher than was observed in the field. 
When plots of simulated female deer movement paths were reviewed, some individuals 



81 



were finding and concentrating their movements in tree islands and not moving into the 
prairies, indicating a need to reevaluate some of the movement algorithms and 
parameters. 

For the subsequent simulation experiment, 4) was increased, and Ahpr, A-tre, and 
AwsA. and A^^n were decreased. Because cypress and pine habitats were a minor 
component of the habitat map and not this focus of the study, A^ys and Apn^ were 
combined as A^-yp in future experiments. 



Table 4.11, Mean percentage of radio-locations in each habitat for each relative affinity 
score from the second calibration experiment for the 6"* year of simulation. 



^HPR 



^TRE 



^WSA 



Ac 



YS 



»^PIN 



'^MAN 



Habitat' 



Factor Levels WPR HPR TRE WSA CYP 



1 
10 



33 

32 



34 

32 



19 

20 



4 

3 



MAN 



20 


34 


28 


21 


4 


4 




30 


30 


38 


18 


3 


2 




20 


36 


37 


11 


4 


3 




50 


29 


29 


29 


3 


2 




30 


33 


34 


20 


3 


3 




50 


31 


32 


20 


4 


3 ] 




5 


32 


34 


20 


4 


1 ] 




15 


32 


32 


19 


4 


5 ] 




5 


32 


34 


20 


4 


2 1 




15 


33 


33 


19 


3 


4 1 







2 



' WPR=wet prairie, HPR=herbaceous prairie, TRE=tree island, WSA=willow/dense 
sawgrass, CYP=cypress/pine, MAN=mangrove/mangrove-prairie transition. 



... •. , - ^ 82 

4.4. Final Movement Model 

The model for adult females and for adult males was finalized after calibration 
with the observed field data through a series of simulation experiments. The final 
algorithms, parameter values, and factor weights used in the movement decisions were 
determined through experimentation during the model calibration (Appendices C and D). 
Several algorithms were changed from the initial description in Section 4.2, so all 
movement algorithms were described in the following sections for completeness. 

Because deer could not move off the map, the habitat map was considered a 
closed environment. Initial locations of simulated deer were located randomly in the 
study area at least 1.5 km from the perimeter of the habitat map (Fig. 4.9); however, there 
was no 'repelling force' to prevent them from moving towards the edge of the map. 

Simulated deer made multiple movements over a 5-day interval, the interval over 
which simulated 'radio-locations' were taken. Each movement was a two-stage process. 
In the first stage of each movement iteration, the deer moved a maximum of one pixel in 
any direction, using 60-m pixels (Fig. 4.5). During this stage, the deer evaluated its 
surroundings and determined the probability of moving to each pixel based on habitat, 
water depth, and relative location in its home range. The second stage consisted of 
selecting a 20-m pixel inside the 60-m pixel and was based solely on habitat and water 
depth. Females made 200 two-stage moves per 5-day interval, and males made 250 two- 
stage moves per 5 -day interval. 



83 






l__ 



>-^ 







16 Kilometers 



A^^ BCNP / ENP boundary 
labitat Classifications 

I Wet Prairie 

I Herbaceous Prairie 
^1 Tree island 

I Willow/dense sawgrass 

I Dwarf cypress prairie 

I Cypress strand 

I Pine 
H Mangrove/prairie transition 
IH Mangrove 




Figure 4.9. Starting locations of simulated deer were located randomly within the solid 
black line (approximately 1.5 km from edge of habitat map). 



84 



4.4,1, 60-in Movement Stage 

Each 20-m pixel was assigned a relative affinity score based on habitat contained 
within the pixel (Table 4.12). A habitat relative affinity score for a 60-m pixel was 
determined using the mean relative affinity of the nine 20-m pixels contained within it. 



Table 4.12, Habit at relative affinity scores for the final simulation mod el. 

Relative affinity 
Female Male 



Habitat 



Wet prairie 


10 


10 


Herbaceous prairie 


10 


35 


Tree island 


35-i: 


KMI 


Willow/dense sawgrass 


40 


15fl\ 


Cypress prairie/strand 


7.5 


^. > . f ■ « 


Pine 


7.5 


5 


Mangrove 


10 


5 



Water depth in each 60-m pixel was calculated as the mean water depth of the 
nine 20-m pixels contained within it. A relative affinity score for each 60-m pixel was 
calculated as 



affinity J = ' 



a 



a- 1 



a 



\y- fiJ 



(depth - fi) 



1 



if depth < fi 

ify9< depth < y 
if depth > y 



fory = 1, 2, 3, . . . , 9 and where a=20, P=10 cm, and y=40 cm for females and a=10, 
P=30 cm, and y=60 cm for males (see Fig 4.6). 

In addition to evaluating habitat and water depth in the current and the adjacent 
pixels, deer used information on habitat and water depth fi-om pixels in the vicinity of its 



85 

current location, but not adjacent to its current location (Fig. 4.10). The simulated deer 
used the information regarding 'long-distance habitat' and iong-distance water depth' in 
these pixels to influence movement to the adjacent pixels. 




N 

ii 



Figure 4.10. Calculation of relative affinities using pixels farther than the pixels adjacent 
to the current location of a hypothetical deer (center 60-m pixel marked with a large X). 
Each small square is a 60-m pixel, and the colors represent relative affinity scores 
assigned to each 60-m pixel (based on either habitat or water depth). A deer could move 
to any of the eight immediately surrounding 60-m pixels or stay in its current pixel. For 
each of these neighboring pixels, the 'long-distance' relative affinity was the mean 
affinity of the nine 60-m pixels associated with it. For example, the long-distance relative 
affinity for the pixel southwest of the current location of the deer (horizontal hatch marks) 
was the mean affinity score of the nine pixels fiirther southwest (diagonal hatch marks). 



96 

The homing beacon algorithm provided simulated deer with an affinity for pixels 

closer to their homing beacon, ( JChome '>'home ) • ^^ location of the homing beacon, based 
on 24 previous radio-location coordinates, was updated every 5 days using the moving 
averages: 

yuomc = —{y, + y,-i + y,-2+----^y,-2i) 

where {x,, y,) were coordinates of the most recent radio-location, and (x,.,, >',.,) were 
coordinates of the radio-location taken 5 days earlier, etc. This window of time used to 
calculate the location of the homing beacon encompassed the 24 previous radio-locations. 
The relative affinity scores for the nine pixels to which the deer could move were 
based on the direction of travel from the current location of the deer to the homing beacon 
(Fig. 4. 11). The strength of the beacon, 6 (equal to 1, (j), or (j)^), was reduced exponentially 
as a deer moved closer to its homing beacon: 



affinity j = ' 



^^^ if z < // 
S otherwise 



fory = 1, 2, 3, . . . , 9, and where J or S^" was the relative affinity score, ji was the 
distance from homing beacon at which the relative affinity was constant, and z was the 
distance from current location to homing beacon. For females and males, \i=500 m. 

By altering the value of 4) over the course of an annual cycle, seasonal changes in 
movement patterns were simulated. For females, (t>=4 when water depth at P-34 (the 
gauging station) was >0 cm, and (|)=3 when water depth at P-34 was <0 cm, enabling 



87 
them to travel farther during the dry season to simulate an expanding search for forage. 

For males, the value of 4) decreased during rut to simulate the search for females. From 
November through May, ({)=3. During June, as males came into the rutting season, <|)=2.5. 
During the peak of rut, from July to September, ^=2. During October, as the rutting 
season concluded, (t)=2. 5. • , .. .} i 



(a) 








(b) 








(c) 








1 


1 


1 




I 


4) 


4) 




1 


4) 


4) 


N 
A 


* 


4) 


4) 


1 


4) 


4) 


4) 


4)^ 


4>^ 


^ 


4> 


4) 


1 


4) 


4) 


4> 


4)^ 


4)^ 



Figure 4.11. Illustration of homing beacon relative affinity calculations, with the homing 
beacon located southeast of current location [center pixel of (a), (b), and (c)]. Affinity 
scores to move (a) towards the south and (b) towards the east are multiplied to give (c) 6 
(equal to 1, 4), 4)^) which was used to calculate the relative affinity scores of moving to 
each of nine possible pixels. 



The pixel memory algorithm gave simulated deer a stronger affinity for previously 
visited pixels than for unfamiliar pixels. Pixels visited in the immediate past were 
avoided to prevent deer from moving to habitat with a high affinity (e.g., tree island) and 
not venturing out of that habitat patch. For females, the relative affmity score for pixely 
was defined as 

0.5 visited in previous 40 steps 
affinity J = i 5.0 visited in previous 30 days (but not in previous 40 steps) 
1 .0 not visited in previous 30 days 



88 

fory = 1, 2, 3, . . . , 9. For males, the relative affinity score for pixely was defined as 



affinity J = ' 



0.5 visited in previous 125 steps 

5.0 visited in previous 30 days (but not in previous 125 steps) 

1 .0 not visited in previous 30 days 



... ' i. , . 
fory = l,2,3,...,9. 

The relative affinity scores for each pixel for each of the six factors (i.e., habitat, 

long-distance habitat, water depth, long-distance water depth, homing beacon, and pixel 

memory) were standardized by converting them to probabilities: 

Pij - ~9 
7=1 

fory = 1, 2, 3, . . . , 9 and where p^ was the probability of moving to pixely for factor / and 
affinity ij was the relative affinity score for pixel 7 for factor /. 

For each of the nine pixels to which the deer could move, the probabilities for 
moving to a pixel based on habitat (i.e., habitat inside the pixel under consideration and 
habitat in the nine ' long-distance' pixels) or water depth were combined using a weighted 
average. For females, the weighted averages for habitat and water depth were 

/'habitat ~ \^° ^ ^adjacent habitat / ''" \^-^ ^ /'long-distance habitat j 
/'water ~ ^^0.8 X ^adjacent water / "'' \0.2 X Piong-distance water j 

Because males have a stronger affinity for wooded areas than females and tend to travel 
farther, 'long-distance habitat' and 'long-distance water' were weighted more heavily 



when calculating the probability of moving to a given pixel based on habitat or water 
depth: 

/'habitat ~ ^U.O X /'adjacent habitat / "•" ^0.4 X /'long-distance habitat / 
/'water ~ \yOX /^adjacent water / "'" ^"-4 X Pjong-distance water / 

During the first 4 months of the simulation, deer initialized their memories for the 
homing beacon and pixel memory algorithms. The probability of moving to/'' (j = 1, 2, 3, 
. . . , 9) pixel was calculated as 

^J = (0-45x ;;habita.)+ (0.45X p^^.^Jf (o.lOX PHo™ng^,„„) 



for females, and as ; ■: 

^J = (0-45 X Phabitat ) + (0.45 X p^^^ ) + (0.05 X /^Homing beacon ) + (O-OS X p 



pixel memory 



for males. Throughout the remainder of the simulation the probability of moving to they"" 
(/' = 1, 2, 3, . . . , 9) pixel was calculated as 

^J = (0-25x p,3,.,.)+ (0.25X /Plater )+ (0.25X PHomingbeacon)+ (0.25X Ppi,„_„^) 

for females. For males, the weights of the four factors depended on biological season. For 
most of the year, the four factors were weighted as 

^j = (0-35x /.,ab.uj+ (0.15x plater )+ (0.25x P,o^„, ^„ ) + (o.25 X /.,.,,_J 

However, during rut (July, August, and September), simulated males had a reduced 
weighting of habitat and an increased weighting of pixel memory on their movement 



90 

decisions; therefore, the four factors were weighted as 

Kj = (0.23X PhabiU.)+ (012X p,^,^J+ (0.25X Phomingbeacon)+ (0-40x Ppj^el memo,y ) 

Each deer chose a 60-m pixel for its next location based on a random draw from the 
multinomial distribution (tt,, 712, JI3, . . . , k,). 
4,4.2. 20-m Movement Stage 

The nine 20-m pixels contained inside the 60-m pixel were evaluated based on 
habitat and water depth. For females and males, probabilities of moving to each 20-m 
pixel were calculated from relative affinity scores for habitat and water depth, and the 
probabilities of moving to each pixel were calculated as 

1 



K - :;{plj ^ p'2j) 



where p y andp y were the probabilities of moving to they* 20-m pixel based on habitat 
and water depth, respectively. The deer selected a 20-m pixel based on a random draw 
fi-om the multinomial distribution (k',, Tt'j, n'j, . . . , 7t',). 

4.5. Evaluation Approach for the Final Movement Model 

To evaluate performance of the fmal model, 50 runs of the simulation for females 
and 50 runs of the simulation for males (each consisting of 30 individuals) were 
conducted using the final model parameterization detailed in Section 4.4. Analyses of the 
final models were done separately for each gender. 

For bum-in evaluation, the armual outcome measures of home range size, distance 
between consecutive home range centers, mean distance between consecutive locations, 
and percentage of locations in each of the four major habitats (wet prairie, herbaceous 



91 

prairie, tree islands, and willow/dense sawgrass) were used. For each run of the 
simulation, bum-in time was estimated, and based on these results, a bum-in time for the 
simulation model was determined. 

Once bum-in time was established for the final model, performance was evaluated 
using data from the T' year after completion of simulation bum-in. The mean armual 
outcome measures of home range size, distance between consecutive home range centers, 
mean distance between consecutive locations, and percentage of locations in each of the 
habitats (wet prairie, herbaceous prairie, tree islands, willow/dense sawgrass, 
cypress/pine, and mangrove) from the simulation were compared to the observed mean 
annual outcome measures from the field data. Also, comparisons were made on a 
hydrologic season basis, using the seasonal outcomes of home range size, distance 
between consecutive locations, and percentage of locations in each of the four major 
habitats (wet prairie, herbaceous prairie, tree islands, and willow/dense sawgrass). 
Simulated deer that were radio-located in the cypress/pine or mangrove habitats were not 
included in calculation of mean percentage of locations in the four major habitats. These 
comparisons were performed using a predictive p-value analysis (Section 4. 1 .6) in which 
the likelihood of the value of the observed outcome (i.e., mean from the field data) arising 
as an outcome of the simulation was assessed. 

4.6. Evaluation of the Final Movement Model for Females 

Variability in outcome measures was high both among individuals (Figs. 4.12 and 
4.13) and among simulation mns (Figs. 4.14 and 4.15). However, the variation in 
outcomes was much larger among individuals within a simulation than among means for 
each simulation mn. Because of heterogeneity in habitat across the study site, a simulated 



92 
deer placed in one area of the map may have different habitat-use patterns than a deer 
placed several kilometers away. The impact of habitat heterogeneity on the variance of 
the outcome measures was minimized as the number of simulation runs increased. 

Of the 50 simulation runs, 56% required no bum-in period (i.e., no significant 
linear trend over time), 24% had a bum-in time of 1 year, 10% had a bum-in time of 2 
years, 6% had a bum-in time of 3 years, and 4% had a bum-in time of >4 years. Based on 
these results, data from the 4"" year of simulation were used to evaluate the final model. 

Home range size and distance between consecutive measurements initially 
decreased from the V year to the 2"^ year and then stabilized for the remainder of the 
simulation. This was due primarily to the fact that the home range algorithms had less 
weight in the movement decision during the first 4 months of the simulation then they did 
during the rest of the simulation mn. The outcome measures that required the most time 
to stabilize were the percentages of observations in wet prairie and in tree islands. On 
average, percentage of observations in the tree islands tended to increase and percentage 
of observations in wet prairie tended to decrease for the first several years of the 
simulation. This trend was not present in all mns of the simulation (e.g., the simulation 
run depicted in Fig. 4.12 and 4.13). For this randomly selected run, several individual 
deer showed an increase in percentage of observations in tree islands, and one showed an 
increase in percentage of locations in the herbaceous prairie; but most deer appeared to 
exhibit consistent habitat-use patterns over time. For this particular experimental mn, 
there was no significant linear trend over time (i.e., no bum-in period) for any of the 
outcome measures. 



93 




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97 

Having established bum-in time for the final model, the performance of the model 
was evaluated (Table 4.13). Using data from the 4* simulation year, predictive p-values 
were calculated to evaluate the likelihood of the values of the observed outcomes arising 
as realizations of the fmal simulation model (Table 4.14). Additionally, histograms of the 
summary outcomes were plotted with the observed field data means (Figs. 4.16, 4.17, and 
4.18). 

Annual home range sizes from the simulation tended to be slightly larger than the 
observed mean home range size by 25 to 50 ha. Distance between annual home range 
centers fi-om the simulations compared favorably with the observed mean distance 
between home range centers. Mean distance between consecutive locations fi-om the 
simulations tended to be smaller than the observed mean distance between consecutive 
locations by approximately 100 m. Habitat use (represented by mean percentage of 
observations in the six habitats) also was comparable to the observed field data, and the 
predictive p-values indicated a high likelihood that the values of the observed mean 
percentages could have arisen from the simulation model. 

On a hydrologic season basis, there was an increase in home range size and mean 
distance between consecutive locations from the wet to the dry seasons, as observed in 
the field data; however, the seasonal shift was not as large as expected. Habitat use, based 
on percentage of observations in each habitat, was similar to that seen in the observed 
data. Observed females did not exhibit any significant shift in habitat use seasonally, and 
the simulated data followed this pattern also. 



H 



n 

Based on the predictive p-value analysis, the simulation model performed well for 
all the outcome measures except for home range size and mean distance between 
consecutive locations. Average home ranges sizes produced by the simulation model were 
comparable to those observed in the field during the dry season, and simulated deer had 
smaller home ranges during the wet season. However, the shift in home range size fi-om 
the dry to the wet season was not as large as expected based on the observed field data. 
This reduced size of the seasonal shift probably impacted the annual home range sizes as 
well, leading to larger then expected home range sizes. However, the size of these 
discrepancies was relatively small (<50 ha). 

The discrepancy in mean distance between consecutive locations between the 
observed and simulated deer was much larger. However, this model lack-of-fit was not of 
great concern for two reasons. First, this measure had no biological meaning. Straight-line 
distance between two consecutive radio-locations was used principally as an indicator of 
the minimum distance a deer traveled over a 5-day interval. Second, the distribution of 
the straight-line distance between two consecutive radio-locations of the observed deer 
was extremely skewed to the right (Fig. 3 .2). A more appropriate measure of central • ; 
tendency may have been the median, instead of the mean. To evaluate this hypothesis, the 
median distance between two consecutive radio-locations was calculated for each 1 ' 
observed deer for each of the annual cycles and for each of the hydrologic seasons. The 
new outcome measure for the field data was the weighted average of the median 
distances. Average median distances were also calculated for each of the 50 simulation 
runs for the annual cycle and for the wet and dry hydrologic seasons in the 4"' year of the 
simulation. For the calibration data, the average median distance between two 



99 



Table 4.13. Mean outcome measures from the 4* year of 50 simulation runs (each with 

30 females) using the final parameterization of the simulation model. 

Outcome measure Annual Wet season Dry season 



Home range size, ha 


298 


(2y 


269 


(2) 


307 


(2) 


Distance between consecutive centers, m 


323 


(6) 




b 






Distance between consecutive locations, m 


582 


(1) 


570 


(2) 


595 


(2) 


Percentage of observations in each habitat 














Wet prairie 


53 


(0.8) 


59 


(0.8) 


60 


(0.8) 


Herbaceous prairie 


14 


(0.4) 


15 


(0.5) 


14 


(0.4) 


Tree islands 


17 


(0.5) 


16 


(0.5) 


16 


(0.5) 


Willow/dense sawgrass 


9 


(0.2) 


10 


(0.3) 


11 


(0.3) 


Cypress/pine 


5 


(0.3) 










Mangrove 


2 


(0.2) 











Standard error in parentheses. 
*■ Outcome measure not evaluated for wet and dry hydrologic seasons. 



Table 4.14. Predictive p-values from the 4* year of 50 simulation runs (each with 30 

females) using the final parameterization of the simulation model. 

Outcome measure Annual Wet season Dry season 



Home range size, ha 


0.02 


0.00 


0.48 


Distance between consecutive centers, m 


0.34 


a 


_ 


Distance between consecutive locations, m 


0.00 


0.00 


0.00 


Percentage of observations in each habitat 








Wet prairie 


0.50 


0.32 


0.28 


Herbaceous prairie 


0.08 


0.18 


0.28 


Tree islands 


0.48 


0.44 


0.28 


Willow/dense sawgrass 


0.44 


0.28 


0.30 


Cypress/pine 


0.34 


• 


* 


Mangrove 


0.50 


- 


- 



' Outcome measure not evaluated for wet and dry hydrologic seasons. 






toe 




Xausnbajj SAqeis^ 



101 



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3 



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f 
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0.0 ■■ 




200 225 250 275 300 325 350 
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0.2 



o 

3 
I 

.a 0.1 
s 



0.0 -' 




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Distance btw. consecutive locations, m 



0.2- 



c 

3 



4) 

■I 0.1 

<u 
IT 



0.0 




40 45 50 55 60 65 70 75 
Percentage of observations In WPR 




5 10 15 20 25 

Percentage of observations In HPR 





10 



12 



14 



16 



Percentage of observations in TRE Percentage of observations in WSA 

Figure 4.17. Distributions of mean wet hydrologic season summary outcomes from 50 
runs (each with 30 females) of the final simulation model. Heavy vertical line represents 
the mean wet hydrologic season summary outcome from the field data. Note- WPR = wet 
prairie, HPR = herbaceous prairie, TRE = tree island, WSA = willow/dense sawgrass 



102 



c 
o 

a- 



0.2 



0.1 



0) 



0.0 ■" r 




200 225 250 275 300 325 350 
Home range size, ha 



0.2- 

>. 

u 

c 
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JL 






i 



550 575 600 625 650 675 700 

Distance btw. consecutive locations, m 



0.2 



c 

.1 0.1 1 



0.0 •* r 




40 45 50 55 60 65 70 75 
Percentage of observations in WPR 




5 10 15 20 25 

Percentage of observations in HPR 




Percentage of observations in TRE 




6 8 10 12 14 16 

Percentage of observations in WSA 



Figure 4.18. Distributions of mean dry hydrologic season summary outcomes from 50 
runs (each with 30 females) of the final simulation model. Heavy vertical line represents 
the mean dry hydrologic season summary outcome from the field data. Note: WPR = wet 
prairie, HPR = herbaceous prairie, TRE = tree island, WSA = willow/dense sawgrass 



103 



0.2 

c 
e 

I 

•I 0-1 



0.0 




475 500 525 550 575 600 625 

Annual 



0.2 

c 
a 

C7 

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a 

q: 



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475 500 525 550 575 600 625 

Wet season 



0.2- 



c 

3 



o 
.> 0.1 



a 

a. 



0.0 




475 500 525 



550 575 600 625 



Dry season 

Figure 4.19. Distributions of average median straight-line distance between consecutive 
radio-locations from 50 runs (each with 30 females) of the final simulation model. Heavy 
vertical line represents the average median straight-line distance between consecutive 
radio-locations fi-om the annual cycle, wet hydrologic season, and dry hydrologic season 
from the calibration data. 



104 
consecutive locations was 564 m (se=23) for the annual cycle, 548 m (se=24) for the wet 

season, and 627 m (se=34) for the dry season. For the simulation data, the average median 
distance between two consecutive locations was 534 m (se=2) for the annual cycle, 523 m 
(se=2) for the wet season, and 546 m (se=2) for the dry season. The predictive p-values 
for the median distances were 0.00 for the annual cycle, 0.06 for the wet season, and 0.00 
for the dry season (Fig. 4.19). These predictive p-values still indicated the likelihood of 
the values of the observed summary outcomes arising as realizations of the simulation 
model was still small, with respect to median distances between consecutive locations. 
However, the discrepancy between the observed and simulated outcomes was much 
smaller (<50 m) than it was using the mean distance between consecutive locations (>100 
m). In retrospect, the median would have been a better measure of central tendency for 
comparison between the observed and simulated data. 

4.7, Evaluation of the Final Movement Model for Males 
To evaluate the performance of the final model, 50 runs of the simulation for 
males were conducted using the final model parameterization detailed in Section 4.4. The 
annual outcome measures that were evaluated included home range size, distance 
between consecutive home range centers, mean distance between consecutive locations, 
and percentage of locations in each of the four major habitats (wet prairie, herbaceous 
prairie, tree islands, and willow/dense sawgrass). Again, the variability in outcome 
measures was higher among individuals (Figs. 4.20 and 4.2 1 ) than it was among 
simulation runs (Figs. 4.22 and 4.23). 



105 




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109 
For each run of the simulation, bum-in time was established. Of the 50 simulation 
runs, all required at least 1 year to reach a steady state. Forty-four percent had a bum-in 
time of 1 year, 24% had a bum-in time of 2 years, 20% had a bum-in time of 3 years, 8%) 
had a bum-in time of 4 years, and 4% had a bum-in time of ^5 years. Further examination 
of the runs that had long bum-in times indicated that the rate of change of the outcome 
measure (i.e., the linear regression slope) was small even though it was statistically 
significant. Based on these results, data from the 4"' year of simulation were used to 
evaluate the final model. 

Home range size and distance between consecutive measurements demonstrated 
an initial decrease fi-om the 1" year to the 2"'' year and then stabilized, which was due 
primarily to the fact that the home range algorithms were weighted lightly for the first 
several months of the simulation. However, the decrease was more drastic than the 
decrease observed in the female simulation runs (Fig. 4.14). For the first several years of 
the simulation, percentage of observations in wet prairie decreased and percentage of 
observations in tree islands increased. This trend was not present for all deer (e.g., the 
simulation run depicted in Fig. 4.20 and 4.21). For this randomly selected mn, most deer 
showed a decrease in home range size and average distance between two consecutive 
locations from the P' to the 2"'' year of the simulation. Although not as evident in the plot, 
there was also a decrease in the distance between consecutive centers fi-om the P' to the 
2°** year of the simulation. For this simulation mn, the bum-in time for each of these three 
outcomes was 1 year. For this same simulation run, individual deer showed changes in 
habitat use (i.e., percentage of locations in each habitat) over the 10-year simulation; 



r .* 



no 

however, the averages were consistent over time as there was no significant linear trend 
overtime (i.e., no bum-in time). ' ' ' -^ 

The performance of the model was evaluated using data from the 4* year of 
simulation (Table 4.15). Predictive p-values were calculated to evaluate the likelihood of 
the values of the observed summary outcomes (i.e., means from the field data) arising as 
realizations of the final simulation model (Table 4.16). Additionally, histograms of the 
simimary outcomes were plotted with the observed field data (Figs. 4.24, 4.25, and 4.26). 

Annual home range sizes and distance between armual home range centers fi-om 
the simulations for males were slightly greater than the observed outcome measure. Mean 
distance between consecutive locations fi-om the simulations tended to be less than the 
observed mean distance between consecutive locations by approximately 150 m. Habitat 
use (represented by mean percentage of observations in each of the six habitats) was 
comparable to the observed field data, and the predictive p-values indicated a high 
likelihood that the values of the observed percentages could have arisen fi-om the 
simulation model. 

The simulation model for males consistently resulted in home ranges sizes and 
distances between annual home range centers that were greater than expected based on 
the observed data. If the model was parameterized so that males had smaller home ranges 
and a shorter distances between annual centers, then several other outcomes were 
adversely affected. Habitat-use patterns shifted to a heavier use of tree islands and 
willow/dense sawgrass. Because of restrictions on home range size and the strong affinity 
for wooded habitat, males would tend to focus their movements in those areas, with little 
incentive to move into the prairies. As a result, movement patterns of simulated males 



* - :'■;■' 



'-•'.■ r*'.^/ • 111 

Table 4.15. Mean outcome measures from the 4* year of 50 simulation runs (each with 



Outcome measure 




Aimual 


Wet season 


Dry season 


Home range size, ha 




351 


(3)^ 


414 


(5) 


270 


(3) 


Distance between consecutive 


centers, m 


365 


(6) 




b 




- 


Distance between consecutive locations, m 


645 


(2) 


696 


(2) 


593 


(2) 


Percentage of observations in 


each habitat 














Wet prairie 




31 


(0.5) 


37 


(0.6) 


32 


(0.6) 


Herbaceous prairie 




20 


(0.5) 


22 


(0.5) 


21 


(0.5) 


Tree islands 




30 


(0.6) 


25 


(0.5) 


29 


(0.6) 


Willow/dense sawgrass 




16 


(0.3) 


16 


(0.3) 


18 


(0.4) 


Cypress/pine 




2 


(0.1) 








» 


Mangrove 




2 


(0.2) 











' Standard error in parentheses. 

'' Outcome measure not evaluated for wet and dry hydrologic seasons. 

Table 4.16. Predictive p-values from the 4* year of 50 simulation runs (each with 30 
males) using the final parameterization of the simulation model. 



Outcome measure Annual Wet season Dry season 



Home range size, ha 


0.06 


0.00 


0.00 


Distance between consecutive centers, m 


0.00 


_a 


_ 


Distance between consecutive locations, m 


0.00 


0.00 


0.00 


Percentage of observations in each habitat 








Wet prairie 


0.08 


0.02 


0.00 


Herbaceous prairie 


0.44 


0.30 


0.28 


Tree islands 


0.18 


0.00 


0.00 


Willow/dense sawgrass 


0.12 


;. 0.38 


0.08 


Cypress/pine 


0.08 


- 


. 


Mangrove 


0.28 


- 


- 



' Outcome measure not evaluated for wet and dry hydrologic seasons. 



•-fmF^' 



112 



•a jii 
13 1 




I 8 



8 

I 
8 

c 
S 

(A 

b 




a: 



a. 




X3uanb8i) 8Age|8^ 



Aouenbajj 8A|)e|3)j 



Aausnbajj 8A|)e|3ij 







S 
in 

a 




0. 

X 



a "O 



- a 






tS 



Xouanbajj SAgeia^ 



^susnbej; 8A|;e|9^ 



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fouonban sadbis^ 



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teuanbajj SAjieiaij 



113 



0.2- 



a) 

I 

> 0.1 
<l> 

en 



0,0 




200 250 300 350 400 450 500 



Home range size, ha 



0.2 

c 

I 
■I 0-1 



0.0 •• 




550 600 650 700 750 800 850 



Distance btw. consecutive locations, m 




0.0 ■" 



15 20 25 30 35 40 45 50 

Percentage of observations in WPR 



0.2- 

& 

c 
to 

Z3 
V 

I 0.11 
w 

0) 



0.0 




10 15 20 25 30 

Percentage of observations in HPR 



0.2 ■ 



c 

0) 

3 

cr 

.a 
a: 



0.1 ■ 



0.0 ■■ r 




10 15 20 25 30 35 40 45 



Percentage of observations in TRE 




Percentage of observations in WSA 



Figure 4.25. Distributions of mean wet hydrologic season summary outcomes from 50 
runs (each with 30 males) of the final simulation model. Heavy vertical line represents the 
mean wet hydrologic season summary outcome from the field data. Note: WPR = wet 
prairie, HPR = herbaceous prairie, TRE = tree island, WSA = willow/dense sawgrass. 



114 



0.2 



0) 



> 0.1 






0.0 ■■ 




200 250 300 350 400 450 500 



Home range size, ha 



0.2 



I 0.1 



0.0-" 




550 600 650 700 750 800 850 



Distance btw. consecutive locations, m 




15 20 25 30 35 40 45 50 

Percentage of observations in WPR 



0.2 

s- 

c 

V 

3 

I 

a 
.i 0.1 

ra 

a: 



0.0 




10 IS 20 25 30 

Percentage of observations In HPR 



0.2 1 

s- 

c 

0) 

3 
(T 

i 

I 0.1 1 

0) 



0.0 -' 




10 15 20 25 30 35 40 45 

Percentage of observations in TRE 



0.2 



« 
a- 

I 0.1 

lU 

a: 



0.0 




10 15 20 25 

Percentage of observations in WSA 



Figure 4.26. Distributions of mean dry hydrologic season summary outcomes from 50 
runs (each with 30 males) of the final simulation model. Heavy vertical line represents the 
mean dry hydrologic season summary outcome from the field data. Note: WPR = wet 
prairie, HPR = herbaceous prairie, TRE = tree island, WSA = willow/dense sawgrass. 



115 
would become increasingly focused on wooded areas, and establishing a steady-state 
would become more difficult. I concluded that a simulation resulting in home ranges and 
distances between home range centers slightly greater than observed in the field was 
acceptable, given the alternative of producing simulations with increased bum-in time or 
simulations that never reached a steady-state. 

As with the simulation results for females, distance between consecutive locations 
for males was less than expected (by >100 m). Again, this measure had little biological 
meaning, and in retrospect, the average median distance was the better measure. For the 
calibration data, the average median distance between two consecutive locations for 
males was 586 m (se=54) for the annual cycle, 761 m (se=67) for the wet season, and 533 
m (se=61) for the dry season. For the 50 final simulation runs, the average median 
distance between two consecutive locations was 581 m (se=2) for the annual cycle, 631 m 
(se=2) for the wet season, and 540 m (se=2) for the dry season. The predictive p-values 
for the median distances were 0.34 for the annual cycle, 0.00 for the wet season, and 0.32 
for the dry season. With respect to average median distance between consecutive 
locations, the likelihood of the values of this observed summary outcome arising as 
realizations of the simulation model was reasonable for the annual cycle and the dry 
season. The model still underpredicted distances between consecutive locations using 
medians for the wet season, but the discrepancy was much smaller than when using 
means. 

Based on the observed data, the decrease in home range size from the wet season 
to the dry season was the same magnitude as expected; however, as discussed previously, 
the size of the home ranges was larger than expected. Mean distance between consecutive 



• 116 
locations also decreased from the wet season to the dry season, as observed in the field 
data; however, the seasonal shifts were not as large as expected and the means were ' 
smaller than expected. Seasonal habitat-use patterns generally followed those expected 
based on the observed data. Relative to the wet season, simulated males increased their 
use of the wooded areas and decreased their use of the wet prairie during the dry season. 
Seasonal shifts in habitat use of the simulated deer were not as great as those of the 
observed deer. Overall, on a seasonal basis, simulated deer were observed more 
firequently in the prairie and less in the wooded areas than expected. 



:/»("'n' ■; 



CHAPTER 5 
WHITE-TAILED DEER MODEL VALIDATION DATA 



The same population of white-tailed deer on the boundary of BCNP/ENP also was 
studied from 1993-1995 (Labisky et al. 1997, MacDonald 1997). The data collected 
during this latter study were used to validate and test the simulation model developed in 
Chapter 4. In August 1992, prior to data collection. Hurricane Andrew moved through the 
study area and caused extensive damage to tree islands. During the collection of the 
validation data, environmental conditions ranged from typical to an extreme, extended 
flood (Fig. 5.1). The fall of 1 994 was extremely wet, with > 1 00 cm of rain occurring 
between August and November, culminating with Tropical Storm Gordon in November 
1 994, which contributed >20 cm of rain. Water levels remained high throughout 1 995. 
5.1. Data Collection and Summary Methods 

White-tailed deer for this study were captured and monitored using the same 
techniques as described for the calibration data collection (Section 3.1). A deer was 
classified as a resident of either BCNP or ENP if ^75% of its radio-locations were in one 
of the management units. 

For the validation data set, data were collected for two annual cycles [1993 (1 
September 1993-31 August 1994) and 1994 (1 September 1994-31 August 1995)]. Deer 
included in an annual cycle were required to have a minimum of 50 radio-locations and 
be monitored for a minimum of 9 months during that annual cycle. 

117 



118 



90- 



60 



-~ 30- 



« 



s 

I 



30 



-60- 



-90 



Observed monthly mean 
Historical monthly means 




Jan 1993 



Jan 1994 



1 

Jan 1995 



Year 



Figure 5.1. Mean monthly water levels recorded at P-34 hydrologic station, and historical 
monthly mean from 1953-1985. Depths were predicted for January 1993 and February 
1993. 



Differences in the measured parameters between hydrologic seasons also were 
estimated. Sufficient radio-telemetry data were collected for 3 hydrologic seasons 
[93DRY (1 November 1993 - 30 April 1994), 94WET (1 May 1994-31 October 1994), 
and 94DRY(FLOOD) (1 November 1994 - 30 April 1995)]. Each included deer was 
required to have a minimum of 30 radio-locations and be monitored for a minimum of 5 
months in each hydrologic season. 

Aimual home range size and seasonal home range size were calculated using the 
95% fixed kernel estimator with least squares cross validation (Silverman 1986, Worton 
1989, Seaman and Powell 1996). Differences between the 2 annual cycles and among the 
3 hydrologic seasons were tested using mixed model analyses with deer as a random 



119 

effect and either year or hydrologic season as a fixed effect. Separate summary statistics 
were calculated and separate analyses were performed for females and males. 

Resource selection was evaluated for each of the 2 annual cycles and each of the 3 
hydrologic seasons using chi-square analyses (Neu et al. 1974, Manly et al. 1993) for 
design U and design 111 studies. The details of these statistical methods were described in 
Section 3.2.1. 

5.2. Data Summary 

The data set used for model validation included 36 adult deer that were captured, 
radio-collared, and monitored between 1993 and 1995 (Appendix E). Twenty-seven deer 
were radio-monitored for 1 year and 9 deer for 2 years. Eight deer were radio-monitored 
for 1 hydrologic season, 18 deer for 2 seasons, and 10 deer for 3 seasons. 
5.2.1. Home Range Size 

Home range sizes for females in 1993 (281 ha, se=38, n=19) did not differ 
(p=0.2021) from home range sizes for females in 1994 (312 ha, se=44, n=10). For males, 
home range sizes in 1993 (248 ha, se=33, n=9) did not differ (p=0.4914) from home 
range sizes in 1994 (302 ha, se=41, n=6). Also, there were no significant changes over 
time when home range size was evaluated on a hydrologic season basis for females 
(p=0.2656) or males (p=0.3092). Female mean home range size was 265 ha (se=42, 
n=19) in 93DRY, 301 ha (se=59, n=18) in 94WET, and 176 ha (se=28, n=l 1) in 
94DRY(FLOOD). Male mean home range size was 166 ha (se=23, n=9) in 93DRY, 217 
ha (se=34, n=7) in 94 WET, and 1 60 ha (se=3 1 , n=6) in 94DRY(FLOOD). 



120 
5.2.3. Habitat Use 

Female habitat-use patterns, based on a simple summary of percentage of 
occurrences in each habitat, appeared to be more strongly affected by the flood conditions 
than male habitat-use patterns (Tables 5.1 and 5.2). During the preflood year (1993), 
females were observed most frequently in the wet prairie; however, during the flood year 
(1994), females used wet prairies less and tree islands more. This same shift in habitat use 
also was observed across hydrologic seasons. Female habitat-use appeared to be 
unchanged from 93DRY to 94WET; however, the percentage of observations of females 
in tree islands increased substantially during 94DRY(FLOOD). For males, the percentage 
of observations in each habitat changed very little from 1993 to 1994. Based on 
percentage of radio-locations in each habitat, little shift in male habitat use was evident 
between 93DRY and 94DRY(FLOOD); however, males were observed in the tt-ee islands 
less and in the wet prairies more during 94WET than during 93 DRY or 
94DRY(FLOOD). 

Based on the selection ratios, similar changes in habitat-use patterns were 
observed. Assuming equal availability of habitat for all individuals, females and males 
exhibited no significant selection for or against any habitat based on the choice of a home 
range (100% MCP) in 1993 and exhibited only moderate selection for specific habitats in 
1994 (Table 5.3). Similarly, on a hydrologic season basis, females and males exhibited no 
significant selection for or against any habitat based on the choice of a home range (100% 
MCP) in 93DRY or 94WET and exhibited only moderate selection for specific habitat in 
94DRY(FLOOD) (Table 5.4). 



121 

Table 5.1. Mean percentage of radio-locations in each habitat for annual cycles for white- 
tailed d eer in BCNP and ENP, September 1993 to August 1995. 

1993" 1994 



Female 




%" 


, 




Wet prairie 


59 


(6)" 


30 


(5) ' 


Herbaceous prairie 


14 


(3) 


20 


(5) 


Tree island 


17 


(3) 


38 


(5) 


Willow/dense sawgrass 


11 


(2) 


10 


(1) 


Dwarf cypress prairie 


<1 


(<1) 


1 


(1) 


Cypress strand 







<1 


(<1) 


Male 










Wet prairie 


21 


(5) 


15 


(3) 


Herbaceous prairie 


19 


(7) 


23 


(6) 


Tree island 


47 


(7) 


49 


(8) 


Willow/dense sawgrass 


14 


(2) 


13 


(3) 


Dwarf cypress prairie 












Cypress strand 













" Sample sizes: female- 1993 (20); female- 1994 (10); male- 1993 (9); male- 1994 (6). 
'' Standard error in parentheses. 

Table 5.2. Mean percentage of radio-locations in each habitat for each hydrologic season 

for white-tailed deer in BCNP and ENP, November 1993 to April 1995. 

93DRY" 94WET 94DRY(FLOOD) 



Female 














Wet prairie 


58 


(6)" 


59 


(6) 


16 


(7) 


Herbaceous prairie 


13 


(3) 


13 


(3) 


19 


(4) 


Tree island 


18 


(4) 


18 


(3) 


57 


(6) 


Willow/dense sawgrass 


11 


(2) 


10 


(2) 


9 


(2) 


Male 














Wet prairie 


15 


(4) 


29 


(8) 


9 


(2) 


Herbaceous prairie 


20 


(8) 


18 


(4) 


20 


(7) 


Tree island 


51 


(8) 


37 


(7) 


59 


(8) 


Willow/dense sawgrass 


15 


(2) 


16 


(3) 


12 


(4) 



Sample sizes: female-93DRY (19); female-94WET (18); female-94DRY (10); male- 
93DRY (9); male-94WET (8); male-94DRY (6). 
'' Standard error in parentheses. 



122 



Table 5.3. Selection ratios and 95% Bonferroni confidence intervals* using the design II 
analysis for habitat inside 100% MCP for each annual cycle for white-tailed deer in 
BCNP a nd ENP, September 1993 to August 1995. 







1993'' 




1994 


Female 










WPR' 


1.02 


(0.85,1.19) 


0.59 


(0.29,0.90) 


HPR 


0.90 


(0.38,1.43) 


2.16 


(1.04,3.28) 


TRE 


1.05 


(0.50,1.59) 


2.22 


(0.63,3.81) 


WSA 


1.00 


(0.61,1.38) 


1.49 


(0.91,1.95) 


Male 










WPR 


0.93 


(0.72,1.15) 


0.86 


(0.68,1.04) 


HPR 


1.09 


(0.36,1.81) 


1.38 


(0.72,2.03) 


TRE 


1.32 


(0.52,2.11) 


1.27 


(0.77,1.76) 


WSA 


1.29 


(0.84,1.73) 


1.43 


(1.08,1.78) 



* Confidence intervals that do not include 1 indicate a selection against (selection ratio 

<1) or a selection for (selection ratio >1) a given habitat. 

" Sample sizes: female-1993 (19); female-1994 (6); male-1993 (9); male-1994 (5). 

" WPR = wet prairie; HPR = herbaceous prairie; TRE = tree islands; 

WSA = willow/dense sawgrass. 



Table 5.4. Selection ratios and 95% Bonferroni confidence intervals* using the design II 
analysis for habitat inside 100% MCP for each hydrologic season for white-tailed deer in 
BCNP and ENP, November 1993 to April 1995. 





< 


?3DRY'' 




94WET 


94DI 


lY(FLOOD) 


Female 












WPR'= 


1.01 


(0.81,1.20) 


0.96 


(0.77,1.16) 


0.52 


(0.25,0.79) 


HPR 


0.84 


(0.32,1.36) 


1.09 


(0.49,1.69) 


2.32 


(1.21,3.44) 


TRE 


1.15 


(0.37,1.93) 


1.20 


(0.52,1.88) 


2.68 


(0.28,5.08) 


WSA 


1.20 


(0.46,1.94) 


0.96 


(0.60,1.32) 


1.33 


(0.82,1.84) 


Male 














WPR 


0.76 


(0.44,1.09) 


0.91 


(0.63,1.18) 


0.64 


(0.28,1.00) 


HPR 


1.32 


(0.21,2.43) 


1.27 


(0.31,2.23) 


2.07 


(0.63,3.51) 


TRE 


2.20 


(0.44,3.96) 


1.26 


(0.32,2.20) 


1.93 


(1.06,2.80) 


WSA 


1.70 


(0.90,2.50) 


1.10 


(0.56,1.64) 


1.44 


(0.60,2.27) 



" Confidence intervals that do not include 1 indicate a selection against (selection ratio 

<1) or a selection for (selection ratio >1) a given habitat. 

" Sample sizes: female-93DRY (19); female-94WET (17); female-94DRY (8); male- 

93DRY (9); male-94WET (7); male-94DRY (5). 

' WPR=wet prairie; HPR=herbaceous prairie; TRE=tree islands; WSA=willow/sawgrass. 



123 

Habitat selection was more pronounced when the selection ratios were based on 
radio-locations with habitat availability assumed equal for all individuals (Tables 5.5 and 
5.6). In 1993, females exhibited selection for tree islands and willow/dense sawgrass and 
exhibited no selection for or against wet and herbaceous prairies. However, in 1994, 
females selected against wet prairie and for tree islands, exhibiting much stronger 
tendencies than in 1993. Using hydrologic seasons, a similar pattern was observed; in 
94DRY(FLOOD), females strongly selected against wet prairie and for tree islands. For 
males, there was little change in the selection ratios from 1993 to 1994. In both years, 
males selected against wet prairie and for tree islands. Little change in the male habitat 
selection ratios was observed across the 3 hydrologic seasons. 

Selection ratios, based on habitat availability within individual home ranges 
(100% MCP), reiterated the changes in habitat use as the flood progressed (Tables 5.7 
and 5.8). Females selected against wet prairies and selected for tree islands more strongly 
in 1994 than in 1993. Additionally, females selected for willow/dense sawgrass areas in 
1993, but exhibited no selection for or against willow/dense sawgrass in 1994, relative to 
the availability in their home ranges. Again, similar patterns were observed across 
hydrologic seasons, with an increasing selection for tree islands and increasing selection 
against wet prairie and willow/dense sawgrass as the flood waters deepened. For males, 
there was little change in the selection ratios on an annual basis or on a hydrologic season 
basis; they consistently selected against wet prairie and selected for tree islands, relative 
to the availability within their home ranges. 






124 

Table 5.5. Selection ratios and 95% Bonferroni confidence intervals' using the design II 
analysis for radio-locations for each annual cycle for white-tailed deer in BCNP and ENP, 
Septemb er 1993 to August 1995. 







1993'' 




1994 


Female 










WPR' 


0.83 


(0.63,1.03) 


0.32 


(0.13,0.51) 


HPR 


0.81 


(0.33,1.28) 


1.50 


(0.50,2.50) 


TRE 


2.41 


(1.34,3.49) 


6.49 


(4.20,8.78) 


WSA 


2.08 


(1.19,2.96) 


1.53 


(0.82,2.26) 


Male 










WPR 


0.29 


(0.12,0.46) 


0.23 


(0.15,0.31) 


HPR 


1.11 


(0.19,2.03) 


1.45 


(0.49,2.40) 


TRE 


6.77 


(4.46,9.08) 


6.56 


(3.72,9.41) 


WSA 


2.81 


(1.92,3.71) 


2.83 


(1.15,4.51) 



^ Confidence intervals that do not include 1 indicate a selection against (selection ratio 

<1) or a selection for (selection ratio >1) a given habitat. 

" Sample sizes: female- 1993 (19); female- 1994 (6); male- 1993 (9); male- 1994 (5). 

' WPR = wet prairie; HPR = herbaceous prairie; TRE = tree islands; 

WSA = willow/dense sawgrass. 



Table 5.6. Selection ratios and 95% Bonferroni confidence intervals' using the design II 
analysis for radio-locations for each hydrologic season for white-tailed deer in BCNP and 
ENP, November 1993 to April 1995. 





< 


)3DRY'' 




94WET 


94DRY(FLOOD) 


Female 














WPR' 


0.81 


(0.62,1.00) 


0.81 


(0.60,1.00) 


0.14 


(0.05,0.23) 


HPR 


0.82 


(0.34,1.30) 


0.85 


(0.44,1.26) 


0.31 


(0.66,1.97) 


TRE 


2.62 


(1.43,3.81) 


2.64 


(1.60,3.68) 


8.65 


(6.97,10.32) 


WSA 


2.05 


(1.04,3.06) 


2.05 


(0.92,3.18) 


1.68 


(0.73,2.63) 


Male 














WPR 


0.20 


(0.06,0.35) 


0.42 


(0.13,0.71) 


0.13 


(0.04,0.23) 


HPR 


1.22 


(0.15,2.28) 


1.26 


(0.54,1.71) 


0.86 


(0.28,1.45) 


TRE 


7.35 


(4.81,9.89) 


5.08 


(2.46,7.71) 


9.27 


(6.90,11.64) 


WSA 


2.91 


(1.81,4.00) 


3.24 


(1.78,4.70) 


2.34 


(0.09,4.59) 



^ Confidence intervals that do not include 1 indicate a selection against (selection ratio 

<1) or a selection for (selection ratio >1) a given habitat. 

'' Sample sizes: female-93DRY (19); female-94WET (18); female-94DRY (10); male- 

93DRY (9); male-94WET (8); male-94DRY (6). 

' WPR=wet prairie; HPR=herbaceous prairie; TRE=tree islands; WSA=willow/sawgrass. 



-.,.125. 

Table 5.7. Selection ratios and 95% Bonferroni confidence intervals' using the design in 
analysis for each annual cycle for white-tailed deer in BCNP and ENP, September 1993 
to August 1995. 







1993' 




1994 


Female 










WPR' 


0.82 


(0.69,0.95) 


0.53 


(0.34,0.71) 


HPR 


0.89 


(0.61,1.17) 


0.71 


(0.32,1.09) 


TRE 


2.29 


(1.40,3.18) 


2.95 


(1.41,4.48) 


WSA 


2.08 


(1.40,2.77) 


1.07 


(0.54,1.60) 


Male 










WPR 


0.31 


(0.16,0.45) 


0.27 


(0.22,0.32) 


HPR 


1.06 


(0.46,1.65) 


1.06 


(0.55,1.57) 


TRE 


5.10 


(2.79,7.41) 


5.17 


(2.99,7.36) 


WSA 


2.19 


(0.95,3.43) 


1.98 


(1.03,2.92) 



" Confidence intervals that do not include 1 indicate a selection against (selection ratio 

<1) or a selection for (selection ratio >1) a given habitat. 

' Sample sizes: female- 1993 (19); female- 1994 (6); male- 1993 (9); male- 1994 (5). 

' WPR = wet prairie; HPR = herbaceous prairie; TRE = tree islands; 

WSA = willow/dense sawgrass. 



Table 5.8. Selection ratios and 95% Bonferroni confidence intervals' using the design HI 
analysis for each hydrologic season for white-tailed deer in BCNP and ENP, November 
1 993 to April 1995. 





( 


J3DRY'' 




94WET 


94DF 


lY(FLOOD) 


Female 












WPR' 


0.80 


(0.70,0.91) 


0.83 


(0.68,0.99) 


0.27 


(0.15,0.38) 


HPR 


0.97 


(0.70,1.25) 


0.78 


(0.49,1.06) 


0.57 


(0.24,0.91) 


TRE 


2.28 


(1.27,3.29) 


2.20 


(1.26,3.14) 


3.21 


(0.72,5.71) 


WSA 


1.71 


(1.02,2.40) 


2.13 


(1.06,3.21) 


1.26 


(0.33,2.19) 


Male 














WPR 


0.26 


(0.12,0.40) 


0.46 


(0.23,0.69) 


0.21 


(0.12,0.29) 


HPR 


0.97 


(0.47,1.48) 


0.90 


(0.50,1.29) 


0.42 


(0.16,0.68) 


TRE 


3.29 


(1.21,5.36) 


4.01 


(2.50,5.51) 


4.81 


(3.05,6.57) 


WSA 


1.70 


(0.53,2.86) 


2.94 


(0.86,5.01) 


1.63 


(0.42,2.83) 



' Confidence intervals that do not include 1 indicate a selection against (selection ratio 

<1) or a selection for (selection ratio >1) a given habitat. 

" Sample sizes: female-93DRY (19); female-94WET (17); female-94DRY (8); male- 

93DRY (9); male-94WET (7); male-94DRY (5). 

' WPR=wet prairie; HPR=herbaceous prairie; TRE=tree islands; WSA=willow/sawgrass. 



126 

5.3. Discussion 

The assumption that extended and extreme high water conditions negatively 
impacted the white-tailed deer population in the Everglades is substantiated by changes in 
survival rates, productivity rates, and spatial-use patterns. 

The survival rates of females during the flood year (48%) were substantially lower 
than the mean annual rate (85%) during 1989-92 (Labisky et al. 1995, MacDonald 1997). 
Male survival rates also decreased during the flood year (54%) relative to the mean 
annual survival rate (67%) during 1989-92 (Labisky et al. 1995, MacDonald 1997). Of 
the adult male mortalities from 1989-92, 76% (16 of 21) occurred as a result of legal or 
illegal harvest, and none of the mortalities during the flood year were related to harvest as 
the hunting season had been cancelled. Thus, the flood did have severe consequences on 
the structure of this deer population. These high mortality rates were comparable to 
mortality rates experienced during previous floods in the Everglades (Loveless 1959b, 
Lampton 1982, Langenau et al. 1984). 

Relative to productivity during 1989-92 and the year prior to the flood, 
productivity appeared to be depressed following the extended flood conditions of 1994-95 
(MacDonald 1997). A decrease in productivity also was observed in 1993 following 
Hurricane Andrew (Labisky et al. 1999). This reduction in productivity may have been 
due to negative impacts of the environmental catastrophes (i.e., flood or hurricane) on the 
physical condition of the females brought on by stress and changes in diet or by an 
increase in predation of neonatal fawns. 

Females demonstrated a substantial shift in habitat use during the flood by 
utilizing tree islands more heavily. This shift may have impacted feeding patterns, as the 



.[ ^^'^ i i^;; J 'iO:j 127 

preferred forage of the female is swamp lily, which is concentrated in the wet prairies. 
Males showed a small increase in use of tree islands from the preflood year to the flood 
year; however, these data also suggest that males were using tree islands more heavily in 
both years than during the normal to dry weather conditions of 1989-92 (calibration data). 
The similarity of habitat-use patterns of females and males during the flood represented a 
severe disruption in the sexually segregated social and spatial patterns of deer (Main et al. 
1996). 

Deer that survived the flood demonstrated high variability in degree of site 
fidelity; however, those that perished during the flood exhibited a low degree of site 
fidelity prior to death (MacDonald 1997). These deer that survived may have had the 
advantage of occupying an optimum location at a slightly higher elevation, thereby 
decreasing the necessity to leave in search of dry ground and forage. Thus, they probably 
were more fit to survive the extended flood conditions because they did not need to 
expend additional energy to find sufficient forage. Deer more familiar with their 
surroundings may be better able to elude predators. Those survivors that exhibited a 
lessor degree of site fidelity during the flood may have been better able to adapt to the 
change in environmental conditions and were successful in finding new home ranges, 
thus increasing the overall fitness of the population. 



CHAPTER 6 
VALIDATION OF THE SIMULATION MODEL UNDER FLOOD CONDITIONS 



In this chapter, I discuss validation of the IBSE simulation model developed in 
Chapter 4 using both visual and statistical tools. I also discuss suggestions for the 
improvement of the model based on the validation results. 

6.1. Approach to Model Validation 

The white-tailed deer movement model was calibrated using radio-telemetry data 
collected on deer that were monitored from 1989 to 1992. To test the model's 
performance under alternative conditions, simulated deer movement patterns were 
evaluated under simulated flood conditions. These patterns were compared to the spatial- 
and habitat-use patterns of the white-tailed deer monitored during the flood of 1994-95 
(Chapters). 

Fifty runs of the simulation were conducted under flood conditions using the same 
set of algorithms and parameter values described for females and males in Section 4.4. 
Each run contained 30 deer started in random locations on the study site map (Fig. 4.9) 
using water depths at P-34 (centrally located water depth gauge), from 1992 to 1995. 

Water depths used in the flood simulations were a combination of observed and 
artificial water levels (Fig. 6.1). As in the calibration simulations, each year corresponded 
to a biological year, which started on April 1. Since the first several years of the 
simulation had water depths that were the average monthly water depths between 1989 

128 • . '.i;'*'' r? •■■ 



M'T;V' i' 



129 



and 1992 [i.e., the same as those used for the calibration runs in Chapter 4 (see Table 
4.2)], I assumed that bum-in time for these simulations was also 3 years. The 3 years used 
for simulation bum-in were YRl-B, YR2-B, and YR3-B (Fig 6.1). Data from the 4"^ and 
following years of the simulation were used in the validation analyses. The 4"" year of the 
simulations (YR4) was used to establish steady-state values for the outcome measures 
prior to the stress of flood conditions, and were comparable to the 4* year of the 
calibration simulations smce monthly water depths were the identical up to this point. 



E 
u 



90 - 



60 - 



30 - 



Tropical Storm Gordon 



o 

m - 

S 
13 

-30 - 



-60 



-90 




. 



"1 1 1 1— 

YRl-B YR2-B YR3-B YR4 



Apr92 Apr93 Apr94 Apr95 YR9 
Year 



Figure 6.1. Monthly water depths at P-34 gauging station used for flood simulations 
Depths for YRl-B, YR2-B, YR3-B, YR4, and YR9 were the mean monthly water depths 
from 1989-91 (same depths as used in model calibration), and years YRl-B, YR2-B, and 
YR3-B constituted the bum-in time for the simulation. From April 1992 to August 1995 
(YR5 through the first half of YR8), observed mean monthly water depths were used. 
Flood conditions were artificially removed during the second half of YR8 by reducing 
water depths. YR9 monthly water depths were the same as those during YRl-B YR2-B 
YR3-B, and YR4. 



130 

From April 1992 to August 1995 (YR5 through the first half of YR8), actual mean 

monthly water depths at P-34 were used. Flood conditions were decreased artificially 
during the 7 months following August 1995 (the second half of YR8) by reducing water 
depths. The final year of the simulation (YR9) had water levels the same as those during 
the first 4 years of this simulation and the same as those in the calibration simulations. 

Several analyses were performed to evaluate the simulation under flood 
conditions. First, plots of the outcome variables were used to examine trends over time. 
Second, predictive p-values were used to evaluate the likelihood that the values of the 
observed summary outcomes (e.g., female mean home range size from 93DRY obtained 
fi-om the field data) could have arisen as an outcome of the simulation model for the 
hydrologic seasons of 93DRY, 94 WET, and 94DRY(FLOOD). Finally, data from the 4* 
year of the simulation were compared to data fi-om the 9* (final) year of the simulation, 
using mixed model analyses, to determine if the simulation had enough robustaess for the 
summary outcomes to return to their preflood values. 

In the following analyses, I focused on outcomes measured for each hydrologic 
season. Due to rapidly fluctuating water levels, changes in spatial- and habitat-use 
patterns were more readily observed with shorter time spans. Also, the annual cycles used 
for the calibration and validation data analyses were not directly comparable. Due to 
timing of commencement and completion of data collection, an annual cycle from April 
to March was used for tiie calibration data set, and an annual cycle from September to 
August was used for the validation data. 

The outcomes evaluated for the model validation were home range size and 
percentage of observations in each of the four major habitats (wet prairie, herbaceous 



131 

prairie, tree islands, and willow/dense sawgrass). Because few deer in the validation data 

set were observed for a sufficient length of time to estimate distance between consecutive 
home range centers, this outcome measure was not evaluated in the validation analyses. 
Since mean distance between consecutive locations was determined to be a poor measure 
of goodness-of-fit (Section 4.6), it not used as an outcome measure. ■^-'■.: / ; r ; 

6.2. Model Validation Results 
6.2.1. Females 

Variability in outcome measures among individuals was high (Fig. 6.2), similar to 
results observed under calibration water levels (Figs. 4.12, 4.13). During the 1" year after 
bum-in (the 1 '' year depicted in the plots), many females showed an increase in home 
range size from the wet to the dry hydrologic seasons. This finding was consistent with 
1989-92 field data used for model calibration, in which females had larger home ranges 
during the dry season than the wet season. From 1992 to 1995, seasonal home range sizes 
decreased; however, by the end of the simulation run, home range sizes appeared to be 
increasing. Due to high variability among individual deer, visually discovering any clear 
temporal patterns was difficult. This difficulty was also present for percentage of 
observations in each of the four major habitats. Variation in habitat use was high both 
among individuals and among years. 

Temporal patterns of mean summary outcomes from the 50 simulation runs were 
described through the use of plots (Fig. 6.3). Again, the increase in home range size from 
the wet season to the dry season during the P' year after bum-in was evident. Seasonal 
shifts in home range size were not present between 92WET and 94WET, when home 
range sizes appeared slightly smaller than those observed during the wet season of the P' 



V , ■•-. <. 



<: r .^J-i' 



j t32 




YR4 



92 



93 



94 
Year 



95 



YR9 




Yr4W 



95W Yr9W 



a: ° 



Q- 




Yr4W 92W 93W 94W 95W Yr9W 
Year 



0. 

X 




Yr4W 92W 93W 94W 95W Yr9W 



m 

I- 




Yr4W 92W 93W 94W 95W Yr9W 
Year 



< 

a) 



= ■» 




Yr4W 92W 93W 94W 95W Yr9W 
Year 



Figure 6.2. Monthly water depths and time trends for hydrologic-season home range size 
and percentage of observations in wet prairie (WPR), herbaceous prairie (HPR), tree 
islands (TRE), and willow/dense sawgrass (WSA) for 30 females from the 4"" through 9* 
year of the validation runs. 'xxW refers to the WET season of year 'xx'; unlabeled ticks 
refer to the corresponding DRY season. Each line represents one deer within a single 
simulation run. 



133 




YR4 



92 



93 



94 
Year 



95 YR9 




^ 1 ' 1 T 1 1 1- ,— , 1 I 

Yr4W 92W 93W 94W 95W Yr9W 
Year 



0. 

5 



2 




I I I ' 



Yr4W 92W 93W 94W 95W Yr9W 
Year 



a. 
a. 

I 



s ^ 




Yr4W 92W 



93W 94W 
Year 



95W Yr9W 



l> 




Yr4W 92W 



93W 94W 
Year 



95W Yr9W 



< 



i '^ 



cr> 




Yr4W 



Yr9W 



Figure 6.3. Monthly water depths and time trends for hydrologic-season home range size 
and percentage of observations in wet prairie (WPR), herbaceous prairie (HPR), tree 
islands (TRE), and willow/dense sawgrass (WSA) from the 4'" through 9* year of the 50 
validation runs (each with 30 females). 'xxW refers to the WET season of year 'xx'; 
unlabeled ticks refer to the corresponding DRY season. Each line represents mean 
outcomes for one run. 



if 



134 

year after bum-in. Home range size decreased again during 94DRY(FLOOD) and 95WET 
(the period of worst flooding). For the 3 postflood hydrologic seasons of the simulation, 
home range sizes appeared to return to the preflood sizes and seasonal patterns. 

Temporal changes in habitat use also were more evident when simulation means 
were plotted (Fig. 6.3). Percentage of observations in the wet prairie decreased slightly 
during the 1" several years of the simulation, then decreased dramatically during 
94DRY(FLOOD) and 95WET (the period of worst flooding) before returning to levels 
similar to those preflood. Mean percentage of observations in the herbaceous prairie 
appeared consistent over time except for a decrease in use during 94DRY(FLOOD). The 
temporal trend observed in the mean percentage of observations in tree islands was a 
mirror-image of the temporal trend observed in the mean percentage of observations in 
the wet prairie. Initially, mean percentage of observations in tree islands increased slightly 
each hydrologic season, a dramatic increase was observed during 94DRY(FLOOD) and 
95WET, and was followed by a return to mean percentages similar to those observed 
preflood. No prominent temporal trend was visually discemable in the mean percentage 
of observations in willow/dense sawgrass. 

Trends during 93DRY, 94WET, and 94DRY(FLOOD) were tested against the 
observed field data using predictive p-values (Tables 6.1, 6.2; Figs. 6.4, 6.5, 6.6). The 
predictive p-value analysis indicated a high likelihood that the values of the observed 
summary field data could have arisen as an outcome of the simulation model in 93DRY. 
In 94WET, mean home range sizes produced by the simulation were smaller than 
expected based on the field data; however, the average difference was only 50 ha (17% 
smaller). Despite the differences in home range size, habitat-use patterns (as measured by 



m 

mean percentage of observations in the four major habitats) were similar. In 
94DRY(FLOOD), the period of most severe flooding for which field data were available, 
simulated deer constricted their home ranges and shifted habitat use fi-ora wet prairie to 
tree islands (Table 6.1), but not as much as expected, based on the observed data (Table 
5.2). 

To evaluate the ability of the simulated deer to return to an "initial state" 
following the stress of flood conditions, summary outcomes from hydrologic seasons in 
the 4*^ year (V year following bum-in) and the 9'^ year (same water levels as in the 4* 
year) were compared (Table 6.3). For each of the summary measures, there was a 
significant difference (p<0.01) between the outcomes for the 4* year and the 9* year, 
indicating that the simulation had not returned to its initial state. However, most of the 
differences between the 4"" and P"" years were biologically insignificant. Between the 4"' 
simulation year and the 9"' simulation year, the mean decrease in home range size was 9 
ha (3% decrease fi-om the 4* simulation year), and mean changes in percentage of 
observations in herbaceous prairie and willow/dense sawgrass were <1 percentage point 
(7% and 8% increase, respectively). However for mean percentage of observations in wet 
prairie and in tree islands, the differences were larger. Observations in the wet prairie 
decreased, on average, by 7 percentage points (12% decrease), and observations in the 
tree islands increased, on average, by 5 percentage points (31% increase). Habitat use 
returned to a distribution similar to that observed in the simulation during 93DRY and 
94 WET, the 2 hydrologic seasons immediately preceding the flood (Table 6.1). 



136 



Table 6.1. Mean outcome measures from the 93DRY, 94WET, and 94DRY(FLOOD) 

hydrologic seasons of 50 simulation runs (each with 30 females). 

Outcome measure 93DRY 94WET 94DRY 



Home range size, ha 




252 


(2) 


249 


(2) 


217 


(2) 


Percentage of observations in 


each habitat 














Wet prairie 




53 


(0.8) 


53 


(0.8) 


48 


(0.9) 


Herbaceous prairie 




15 


(0.5) 


15 


(0.4) 


12 


(0.4) 


Tree islands 




21 


(0.6) 


22 


(0.6) 


31 


(0.7) 


Willow/dense sawgrass 




10 


(0.3) 


10 


(0.2) 


9 


(0.2) 



Table 6.2. Predictive p-values from the 93DRY, 94WET, and 94DRY(FLOOD) 

hydrologic seasons of 50 simulation runs (each with 30 females). 

Outcome measure 93DRY 94WET 94DRY 



Home range size, ha 




0.12 


0.00 


0.00 


Percentage of observations in 


each habitat 








Wet prairie 




0.18 


0.12 


0.00 


Herbaceous prairie 




0.30 


0.28 


0.02 


Tree islands 




0.32 


0.10 


0.00 


Willow/dense sawgrass 




0.38 


0.48 


0.46 



Table 6.3. Mean hydrologic season outcome measures from the P' year after bum-in 

(year 4) and the last year (year 9) of 50 simulation runs (each with 30 females). 

Outcome measure Yr 4 WET Yr 4 DRY Yr 9 WET Yr 9 DRY 



Home range size, ha 


271 


(2) 


307 


(2) 


264 


(2) 


297 


(3) 


Percentage of observations 


















in each habitat 


















Wet prairie 


61 


(0.8) 


61 


(0.9) 


54 


(0.8) 


55 


(0.8) 


Herbaceous prairie 


13 


(0.4) 


13 


(0.5) 


15 


(0.5) 


14 


(0.5) 


Tree islands 


17 


(0.5) 


16 


(0.5) 


22 


(0.6) 


20 


(0.6) 


Willow/dense sawgrass 


9 


(0.2) 


10 


(0.3) 


10 


(0.2) 


11 


(0.3) 



137 



0.2- 



0) 

IT 
(D 

O 

■M 0.1 
& 



0.0 -■ 






^ 



I 






yyyb 



^m^wmm 



i 



i^ 






200 



250 



300 



0.2 



g 0.1 
(D 



0.0 



0.2 



c 
I 

9) 



0.1 



0} 



0.0 



Home range size, ha 



I 



^^ 



P^^P^ 



y 



20 



30 



40 



50 



60 



70 



Percentage of observations in WPR 






I 



m^^ 



10 



20 



30 



— I — 
40 



50 



Percentage of observations in TRE 



0.2 



3 

.2 0.1 - 

ra 
o 

a. 



0.0 



^ 



li^ 




L 



^? 



5 10 15 20 

Percentage of observations in HPR 



25 




6 8 10 12 14 

Percentage of observations in WSA 



Figure 6.4. Distributions of mean summary outcomes during 93DRY from 50 simulation 
runs (each with 30 females). Heavy vertical line represents the mean annual summary 
outcome from the field data. Note: WPR = wet prairie, HPR = herbaceous prairie, TRE = 
tree island, WSA = willow/dense sawgrass. 



138 



0.2- 



3 

a> 

■2 0.1 

JO 

o 

q: 



0.0 ■• 




0.2 



c 
o 

I 

(D 

■^ 0.1 



0.0 



0.2 



CT 



■M 0.1 



JO 

o 

a: 



200 250 

Home range size, ha 



300 




Percentage of observations in WPR 



55 



m 



v^. 



0.0- 



A 



m 



y^ 



>A 



^ 
. 



iifc 



10 



20 



30 



40 



50 



Percentage of observations in TRE 




Percentage of observations in HPR 




Percentage of observations in WSA 



Figure 6.5. Distributions of mean summary outcomes during 94WET from 50 simulation 
runs (each with 30 females). Heavy vertical line represents the mean annual summary 
outcome from the field data. Note: WPR = wet prairie, HPR = herbaceous prairie, TRE = 
tree island, WSA = willow/dense sawgrass. 



139 




0.2 



f 



> 1 



0.0-^ 



Home range size, ha 



m 



yi 









11* 



20 30 40 50 60 
Percentage of observations in WPR 



70 




Percentage of observations in TRE 



0.2 



<B 

:g 0.1- 

CD 



0.0 -' r- 



J 



Ik 



5 10 15 20 25 

Percentege of observations in HPR 



0.2 



o 

c 

(S 



JO 

e 



0.0 



L 



^™ 



6 8 10 12 14 

Percentage of observations in WSA 



Figure 6.6. Distributions of mean summary outcomes during 94DRY(FLOOD) from 50 
simulation runs (each with 30 females). Heavy vertical line represents the mean annual 
summary outcome from the field data. Note: WPR = wet prairie, HPR = herbaceous 
prairie, TRE = tree island, WSA = willow/dense sawgrass. 



140 

6.6.2. Males 

Variability in outcome measures among individuals was high (Fig. 6.7), similar to 
results observed under calibration water levels (Figs. 4.20, 4.21). Most simulated males 
had smaller home ranges during the dry season than during the wet season, consistent 
with patterns observed from 1989-92. Variation in home range sizes appeared to be 
greater during periods when deer experienced water deeper than in the calibration 
simulations during rut (i.e., 93WET, 94WET, and 95WET). No temporal trends were 
visually discemable for the percentage of observations in wet prairie, herbaceous prairie, 
or willow/dense sawgrass; however, the percentage of observations in tree islands 
appeared to increase over the span of the simulation run. Variation in habitat use was high 
among individuals and years. 

Temporal patterns of the mean summary outcomes from the 50 simulation runs 
were described through the use of plots (Fig. 6.8). As with female simulations, plots of 
mean summary outcomes were more informative with regard to overall trends than plots 
of individual summary outcomes. Mean home range size was consistently larger during 
the wet seasons than it was during the dry seasons; however, no changes were evident as 
a result of flooding. As with the flood simulations for females, mean percentage of 
observations in wet prairie was a mirror-image of mean percentage of observations in tree 
islands. For the first several years of the simulation (through 94 WET), percentage of 
observations in wet prairie decreased gradually and percentage of observations in tree 
islands increased slowly. In 94DRY(FLOOD), use of wet prairie dropped dramatically 
and use of tree islands increased dramatically. Following 94DRY(FLOOD), percentage of 
observations in wet prairie and in tree islands returned to pre-flood levels. Percentage of . 



141 



90 
60 1 



i 30 



<1> 

ra -30 



-60 
-90 




YR4 



92 



93 



94 

Yaar 



95 



YR9 



E 
o 

X 




Yr4W 92W 93W 94W 95W Yr9W 



^ 5^- 



Year 



a. 
5 




Yr4W 92W 93W 94W 95W Yr9W 
Year 



a. 

I 




-I — ' — 1 — 1 — I — 1 — I — — i- 
Yr4W 92W 93W 94W 95W Yr9W 

Year 



Ui 

q: 



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Yr4W 



YrSW 



< 



S 



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^V^^^s^c^^a^^Kl^ 




^^^^^ 


o . 




o ■ 




^ V^*-^": 





Yr4W 92W 93W 94W 95W Yr9W 



Year 



Figure 6.7. Monthly water depths and time trends for hydrologic-season home range size 
and percentage of observations in wet prairie (WPR), herbaceous prairie (HPR), tree 
islands (TRE), and willow/dense sawgrass (WSA) for 30 males from the 4"' through 9"" 
year of the validation simulations. 'xxW refers to the WET season of year 'xx'; 
unlabeled ticks refer to the corresponding DRY season. Each line represents one deer 
within a single run. 



1^ 



90 

60 1 
30 




ra -30 
-60 
-90 




YR4 



92 



93 



94 
Year 



95 



YR9 



0) 

2 




Yr4W 92W 93W 94W 95W Yr9W 



Year 




Yr9W 



Q. 

X 



S 




Yr4W 



Yr9W 






o 




—I 1 r- 

Yr4W 92W 93W 94W 95W Yr9W 
Year 



< 

CO 



J3 ^ ■ 




Yr4W 92W 93W 94W 95W Yr9W 



Year 



Figure 6.8. Monthly water depths and time trends for hydrologic-season home range size 
and percentage of observations in wet prairie (WPR), herbaceous prairie (HPR), tree 
islands (TRE), and willow/dense sawgrass (WSA) from the 4* through 9* year of the 50 
validation runs (each with 30 males). 'xxW refers to the WET season of year 'xx'; 
unlabeled ticks refer to the corresponding DRY season. Each line represents mean ' 
outcomes for one run. 



143 

observations in herbaceous prairie and willow/dense sawgrass exhibited no discemable 
temporal trends, except for a possible decrease in the percentage of observations in 
willow/dense sawgrass during the periods of deepest water. 

Summary outcomes during 93DRY, 94WET, and 94DRY(FLOOD) were tested 
against the observed field data using predictive p-values (Tables 6.4, 6.5; Figs. 6.9, 6.10, 
6.1 1). The simulation consistently produced mean home range sizes that were larger than 
those observed in the field during 93DRY, 94WET, and 94DRY(FLOOD). The 
simulation performed better, although not perfectly, with respect to mean percentage of 
observations in the four major habitats, hi 93DRY, it was unlikely that values of the 



Table 6.4. Mean outcome measures from the 93DRY, 94WET, and 94DRY(FLOOD) 

hydrologic seasons of 50 simulation runs (each with 30 males). 

Outcome measure 93 DRY 94WET 94DRY 



Home range size, ha 265 (3) 397 (4) 251 (2) 

Percentage of observations in each habitat 

Wet prairie 

Herbaceous prairie 

Tree islands 

Willow/dense sawgrass 



Standard error in parentheses. 



30 (0.8) 


32 (0.8) 


25 (0.7) 


22 (0.6) 


23 (0.6) 


22 (0.6) 


30 (0.6) 


28 (0.6) 


37 (0.7) 


s 18 (0.4) 


17 (0.3) 


16 (0.3) 



Table 6.5. Predictive p-values from the 93DRY, 94WET, and 94DRY(FLOOD) 

hydrologic seasons of 50 simulation runs (each with 30 males). 

Outcome measure 93DRY 94WET 94DRy" 

Home range size, ha 0.00 0.00 0.00 

Percentage of observations in each habitat 

Wet prairie 0.00 0.32 0.00 

Herbaceous prairie 0.34 0.12 40 

Tree islands 0.00 0.00 0.00 

Willow/dense sawgrass O.IO 0.40 02 



144 



0.2 



o 
•5 0.1 

o 



0.0- 









m 



MM 



1 



200 300 400 

Home range size, ha 



500 




10 20 30 40 

Percentage of observations in WPR 




Percentage of observations In TRE 




0.0-^ 



10 15 20 25 30 

Percentage of observations in HPR 




Percentage of observations in WSA 



Figure 6.9. Distributions of mean summary outcomes during 93DRY from 50 simulation 
runs (each with 30 males). Heavy vertical line represents the mean annual summary 
outcome from the field data. Note: WPR = wet prairie, HPR = herbaceous prairie, TRE = 
tree island, WSA = willow/dense sawgrass. 



145 



0.2- 



I 



•S 0.1 



CO-" 



0.2 



9) 

•2 0.1 



0.0 -■ 




200 300 400 500 

Home range size, ha 




10 20 30 40 

Percentage of observations in WPR 




20 30 40 

Percentage of observations in TRE 




0.0 -w 



10 15 20 25 30 

Percentage of observations in HPR 



0.2 

c 

0) 
IT 
i 

■^ 0.1 

JS 
o 



0.0-" f 




10 15 20 25 

Percentage of observations in WSA 



Figure 6.10. Distributions of mean summary outcomes during 94WET from 50 
simulation runs (each with 30 males). Heavy vertical line represents the mean annual 
summary outcome from the field data. Note: WPR = wet prairie, HPR = herbaceous 
prairie, TRE = tree island, WSA = willow/dense sawgrass. 



146 



0.2- 




i 

IS 


s- 




^Mi'i^i 


<D 




^H^^^ 


3 




Hfpl 


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1 




liift 












V''//^//My// 



0.2 

>. 
u 

c 

(D 

3 

ID 

..g 0.1 
JO 
ID 

a: 



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200 300 400 

Home range size, ha 



500 




10 20 30 40 

Percentage of observations in WPR 




20 30 40 50 

Percentage of observations in TRE 




10 15 20 25 30 

Percentage of observations in HPR 



0.2- 

5" 

c 
d) 

3 

a) 

•5 0.1 

ra 

ID 

a. 



0.0-" 




10 15 20 25 

Percentage of observations in WSA 



Figure 6.11. Distributions of mean summary outcomes during 94DRY(FLOOD) from 50 
simulation runs (each with 30 males). Heavy vertical line represents the mean annual 
summary outcome from the field data. Note: WPR = wet prairie, HPR = herbaceous 
prairie, TRE = tree island, WSA = willow/dense sawgrass. 



147 
observed summary outcomes would have arisen as an outcome of the simulation, as the 
simulation produced summary outcomes that overpredicted the percentage of 
observations in wet prairie and underpredicted the percentage of observations in tree 
islands. In 94WET, the simulation model provided better predictions for habitat use than 
in 93DRY. The percentage of observations in tree islands was still less than expected 
based on the observed data, but the discrepancy was not as great as in 93DRY. In 
94DRY(FLOOD), as in 93DRY, the simulation produced summary outcomes that 
overpredicted the percentage of observations in wet prairie and underpredicted the 
percentage of observations in tree islands. The simulation was sensitive to flood 
conditions, as the percentage of observations in wet prairie decreased and percentage of 
observations in tree islands increased during 94DRY(FLOOD), relative to 93DRY and 
94WET (Table 6.4); however these changes were less than those observed in the field 
(Table 5.2). 

To evaluate the ability of the simulated male deer to return to an initial state 
following the stress of the flood conditions, summary outcomes from the hydrologic 
seasons in the 4'" year (P' year following bum-in) and the 9'" year (same water levels as in 
the 4'" year) were compared (Table 6.6). For percentage of observations in willow/dense 
sawgrass, there was no significant difference (p=0.2439) between the outcomes for the 4* 
year and the 9"" year. For the rest of the summary measures, there was a significant 
difference (p<0.05) between the outcomes for the 4"' year and the 9* year, indicating that 
the simulation model had not returned its initial state. However, several of the differences 
between the 4'" and 9"' years were small, even though they were statistically significant. 
Between the 4'" simulation year and the 9'" simulation year, the mean change in home 



148 
range size was 10 ha (3% decrease), and mean change in percentage of observations in 
herbaceous prairie was <1 percentage point (4% increase). For mean percentage of 
observations in wet prairie and in tree islands, the differences were larger. Observations 
in the wet prairie decreased, on average, by 5 percentage points (15% decrease), and 
observations in the tree islands increased, on average by 4 percentage points (19% 
increase). Habitat use approached a distribution similar to that observed in the simulation 
during 93DRY and 94WET, the 2 hydrologic seasons immediately preceding the flood 
(Table 6.1). 



Table 6.6. Mean hydrologic season outcome measures from the 1" year after bum-in 
(year 4) and the last year (year 9) of 50 simulation runs (each with 30 males). 

Outcome measure Yr4WET Yr4DRY Yr9WET Yr9D RY 

Home range size, ha 412 (4) 267 (3) 397 (5) 259 (3) 

Percentage of observations 

in each habitat 



Wet prairie 36 (0.9) 32 (0.9) 31 (0.8) 27 (0.8) 

Herbaceous prairie 22 (0.6) 22 (0.5) 23 (0.6) 23 (0.6) 

Tree islands 25 (0.5) 28 (0.5) 29 (0.5) 33 (0.6) 

Willow/dense sawfflass 17 (0.4) 18 (0.4) 16 (0.3) 18 (0.3) 
Standard error in parentheses. 



6.3. Discussion 

Validation with radio-telemetry data obtained during the flood of 1 994-95 
indicated that the proposed simulation model was sensitive to flood conditions, but also 
revealed the movement patterns of the simulated deer did not shift as much as expected. 
There are several potential reasons that may explain the lack-of-fit of the simulation 
model to the observed field data. 



149 
6.3.1. Quantity and Quality of Validation Field Data 

First, the number of deer included in the validation data set (23 females and 13 
males) was smaller than the number of deer included in the calibration data set (27 
females and 19 males), and many of the deer in the validation data set were monitored for 
a shorter time period. Therefore, the validation data may not have been representative of 
the whole time interval [93DRY, 94WET, and 94DRY(FLOOD)]. For example, in the 
validation data set, only two males were monitored during all 3 hydrologic seasons, and 
four of the six males monitored during 94DRY(FLOOD) were not monitored during any 
other time intervals. 

Simulated deer started the simulation by being randomly placed throughout the 
study area; however, the deer included in the validation data may not have been 
representative of the entire study area (Figs. 6.12, 6.13). Because the boundary between 
BCNP and ENP roughly divides the study area in half, management area residence 
provided an indication of the spatial distribution the radio-monitored deer. For the 
calibration data, 52% (15 of 29) of the females resided in BCNP with the remainder 
residing in ENP, and 24% (4 of 17) of the males resided in BCNP with 6% (1 of 17) 
residing in both management areas and the remainder residing in ENP. For the validation 
data, the females were reasonably divided with 48% (1 1 of 23) residing in BCNP, 22% (5 
of 23) residing in both management areas, and 30%) (7 of 23) residing in ENP. However, 
no males in the validation data set were residents of BCNP whereas 23% (3 of 13) were 
residents of both management areas and 77%. (10 of 13) were residents of ENP. 



v«'> ; . 



150 




1989-92 




93DRY 









> . ■' . • 









i*-^,:.^'.<i. 



•:'•-. :*i 




A 




94WET 






■'!>.-/ f 



^ 

/^-..' 



,- »'- 



94DRY(FLOOD) 

■■■" x*l'i 





16 Klomaitars 



/V BCNP / EHP boundary 



Habitat 

Wet Prairie 
Hert>aceous Prairie 
Tree island 
Willow/dense sawgrass 



I Dwarf cypress prairie 
I Cypress strand 



I Mangrove/prairie transition 
I IMangrove 



Figure 6.12. Home range centers of females included in the calibration data set (1989-92) 
and the 3 hydrologic seasons of the validation data set [93DRY, 94 WET, 
94DRY(FLOOD)]. 



151 




A..^*^:^ 



W^iX 



1989-92 



■/- 













93DRY 



•jic-' 



y 



V'^^ 



■r--- 






. > .■ 



■'■ >. '. 




'I 






k 







16 KlonMters 



/V BCNP / EHP boundary d] Herbaceous Prahle 

^B Tree island 



Habitat ^y| Dwarf cypress prairie 

n Wet Prairie IH Cypress strand 

Pine 

Mangrove/prairie transition 
WiHow/dense sawgrass mH Mangrove 



Figure 6.13. Home range centers of males included in the calibration data set (1989-92) 
and the 3 hydrologic seasons of the validation data set [93 DRY, 94WET, 
94DRY(FLOOD)]. 



152 
Several potentially serious implications of the imbalance in the temporal and 
spatial distributions of the validation data set exist. In the simulation runs, all deer were 
present for all time intervals, but in the validation data, entry and exit from the data set 
was staggered. The staggered entries were due to deer being captured and entered into the 
study at a later date, whereas the staggered exits were due to failed radio-transmitters, 
death, or relocation outside the study area. In addition, the simulated data and the 
validation data may not have represented the same population of deer in a spatial 
framework. Males in the validation data set were heavily biased towards residence in 
ENP whereas simulated males had random starting locations in either management area. 
Thus, comparisons between the simulated flood data and validation data indicated lack- 
of-fit, but perhaps not because the model did an inadequate job of simulating deer 
movement. The lack-of-fit may have been because deer in the simulation were monitored 
for the entire time period and were located throughout the study area whereas many deer 
(especially males) in the validation data set represented fewer than 3 hydrologic seasons 
and only a small portion of the study area. 
6.3.2. Factors Not Included in the Simulation Model 

Habitat and water maps with more detail may have improved the predictive 
abilities of the simulation model. Although the habitat map had an accuracy of 80%, the 
habitat classifications were very broad. Within these broad classifications used by Miller 
(1 993), a great deal of heterogeneity existed within each habitat. For example, no 
distinction was made between hardwood hammocks, which are rarely inundated, and 
:.. bayheads, which are more frequently inundated. Although wet prairies are the most 
species-rich of the Florida marshes (Kushlan 1990), in this application, they were 



153 
considered homogenous both in elevation and in appeal relative to other habitats. An 

example of the complexity of the prairie/tree island/slough landscape was provided by 

Himter's (1990) map of a 112 km^ study area in the Taylor Slough (south central 

Everglades, see Fig. 2.1) which contained > 1 00 habitat classifications. 

The hydrology of the Everglades is not as simple as is portrayed by the temporal 

water-depth map used for these simulations. Although the centrally located water gauge 

(P-34) provided an indication of water depth over the study area, local topography and the 

status of proximate anthropogenic canals and pumps also influenced water depth. A more 

detailed simulation model of Everglades hydrology under natural and current water 

management schemes was developed by Fennema et al. (1994); however, the scale was 

too large to be suitable for the deer movement model presented in this study. 

In addition, inclusion of mortality, as a function of the environment, may have 

improved the predictive capacities of the simulation model. Deer stranded in deep water 

during the Everglades flood of 1994-95 were more likely to either die or emigrate than 

those with access to higher ground and sufficient browse (MacDonald 1997). However, 

those deer that chose to emigrate faced additional stresses due to traveling. These 

movements likely increased their mortality rates, hi the simulation, deer had the 

possibility of emigrating to areas of higher ground, but there was a distinct chance that 

they would never locate high ground. These stranded simulated deer may have spent ^3 

months in 60 cm of water with no ill effects because mortality was not included in the 

model. Some simulated individuals successfully sought and found tree islands during the 

flood, whereas others maintained a consistently high percentage of observations in the 

wet prairie and a negligible percentage (i.e., <5%) of observations in tree islands (see 






Figs. 6.2 and 6.6 for examples). These stranded deer may have impacted the summary 
outcomes for the simulations by increasing the mean percentage of observations in the 
prairie and reducing the mean percentage of observations in the tree islands. If deer that 
were unsuccessful in finding refuge and forage on higher ground had a high probability of 
dying (i.e., being removed from the simulation during the flood), then the summary 
outcome measures for the 'surviving' deer may better represent observations from the 
field. 

To augment the addition of mortality as a ftinction of environment, the inclusion 
of additional population dynamics into the simulation model may have improved its 
predictive abilities. In the current model, the deer population remained static with 30 
individuals (all either female or male) with no interactions among them. Increasing the 
number of deer to observed density levels and including deer-to-deer interactions may 
further improve the credibility of the simulation. Formation of matriarchal groups in 
females and territory defense in males could be added. Mortality, as a function of 
predation, age, and other causes, as well as fecundity could be included in the simulation. 
6.3.3. Issues Involving Movement Algorithms Used in tlie Model 

Although including population dynamics in the simulation may improve the 
performance of the model relative to the validation data, issues involving the current 
algorithms also should be addressed. Efforts should be made to further minimize bum-in 
time. If the number of deer in the simulation was increased to approximate typical 
population densities and interactions among deer were included, the CPU time to 
complete one run of the simulation would drastically increase. As simulation time 
increases, the proportion of computer time allotted to simulation bum-in becomes more 



155 
relevant. A goal of achieving consistent simulation bum-in within 1 or 2 years of 
simulation is realistic, and the best approach is most likely through further 
experimentation with the homing beacon and pixel memory algorithms. The issue of 
bum-in time also becomes more complicated when fecundity is added to the simulation. 
As each new deer is 'added' to the population, it will need time to explore its 
surroundings and create a home range. This additional level of complexity provides 
further motivation to reduce bum-in time. 

Home range size of males also should be addressed, as the simulation tended to 
yield home ranges larger than expected. Smaller home ranges were obtained with 
minimal alteration of simulation parameters, but the trade-off was an increase in bum-in 
time. Again, further experimentation with the homing beacon and pixel memory 
algorithms, and possibly the introduction of additional algorithms, may produce home 
range size estimates closer to the observed field data. Further analyses could be done 
using the existing field data and simulation data to detennine if using the kemel density 
estimator for home range size was appropriate or if a different home range estimator (e.g., 
minimum convex polygon) would be more descriptive, given the spatial distributions of 
the observed and simulated radio-locations. 

A final area of exploration is to further investigate why the simulation outcomes 
did not return to their 'initial' steady-state after flood conditions were relaxed in the 
validation simulations. Although the simulated outcomes moved towards their initial state 
during the year following the flood, they did not retum to that initial state. One hypothesis 
was that the water conditions that existed in the simulation between 92 WET and 93WET 
(after bum-in, but before the flood) moved the model processes to a new, different 



156 
equilibrium. With longer simulation runs and runs using different hypothetical temporal 
water-depth patterns, the temporal dynamics of these movement processes could be 
examined further. 



<; 



CHAPTER 7 
CONCLUSIONS AND FUTURE RESEARCH DIRECTIONS 



The objective of this study was to develop an IBSE simulation model of 
movement patterns of adult white-tailed deer in the Florida Everglades. The model 
provided a means of exploring patterns of spatial use of deer in response to environmental 
catastrophes (e.g., tropical storms) and to different management regimes (e.g., water 
control). While conducting the initial phase of model development, I was unable to locate 
guidelines or a framework for the calibration of an IBSE simulation model. Therefore, a 
major focus of this research became the development and documentation of such a 
process. Although none of the tools used in the calibration process were new, formalizing 
their use in an organized iterative fashion for model development and calibration (Fig. 
4.4) was a pioneering exercise. 

The specific objective of the simulation model was to predict how temporal 
landscape changes (i.e., rising and falling water levels) would affect movement patterns 
of deer in the Florida Everglades. This objective required calibration and validation 
procedures. Calibration issues focused on discrepancy measures to test IBSE model 
output relative to observed data, an iterative approach for calibrating an IBSE model with 
sequential experimentation, and evaluation of the predictive abilities of an IBSE 
simulation using predictive p-values. The algorithms and parameterization of the initial 
model were presented and two of the sequential calibration experiments for females were 

157 



158 
discussed in detail. The final model for females and males was presented and the final 

evaluation, using predictive p-values, was discussed. After the model was sufficiently 

calibrated, validation was performed using radio-telemetry data collected just prior to and 

during the flood of 1994-95. Based on the results of the validation analyses, several 

suggestions for improvement of the movement model were considered. 

7.1. Applications of the White-tailed Deer Movement Simulation Model 

This movement model, after concerns revealed during validation were addressed, 

can be used to predict the status of white-tailed deer in the unstable ecosystem of the 

Everglades. Additional validation could be conducted by assessment of performance of 

the simulation relative to radio-telemetry data collected from white-tailed deer in other 

areas of the Everglades. For example, the model could be run using habitat maps from the 

Taylor Slough area and evaluated with the data collected by Hunter ( 1 990). 

One use of this model is as one of the many tools for planning Everglades 

restoration (Fleming et al. 1994, USGS 1997, DeAngelis et al. 1998). The working 

hypothesis for the restoration program is that a return to natural hydrological conditions 

will result in a substantial recovery of many characteristic and endangered species in the 

region. Part of this large restoration effort has been the development of the suite of 

simulation models. Across Trophic Level System Simulation (ATLSS), to predict and 

compare the effects of alternative hydrologic scenarios on this ecosystem. The movement 

algorithms for deer that 1 developed could be incorporated into the model as a comparison 

to the deer component currently used in the ATLSS model. 

Another potential application of the model would be to predict the impact of 

catastrophic events on white-tailed deer in south Florida. On average, south Florida is 



159 
subjected to a tropical storm once every 3 years. Some of those storms are relatively dry, 
like Hurricane Andrew in 1992, and some are extremely wet, like Tropical Storm Gordon 
in 1 994. Although both storms had a devastating impact on the human population and 
human-built structures, each storm had a different impact on the deer population. This 
simulation model can aid in predicting the level and longevity of the impact on the deer 
population, for various scenarios such as strong hurricanes several years in a row, or 
several hurricanes in a single year. 

7.2. Contributions to the Field of Ecological Modeling 
The set of calibration tools and the iterative approach developed and demonstrated 
in this dissertation provides a framework for more rigorous evaluation of simulation 
models. Although the techniques were presented in the context of IBSE simulation 
models, they could be applied to the development, calibration, and validation of other 
classes of simulation models as well. 

Bum-in time was explored as a nuisance parameter of simulations, and a 
technique for its estimation is presented. During my literature review, I found only one 
IBSE simulation model in which the issue of bum-in was addressed. Risenhoover et al. 
(1997) allowed deer in their simulation to move and interact with the landscape for 1 year 
to provide a realistic dispersion of animals. However, they gave no justification for the 
length ofthe initialization time. ■> ' 

Simulation model building was presented as an iterative process in which the 
developer constantly reevaluates the model and updates algorithms and parameter values 
to obtain the best fit possible. This systematic, iterative approach aids in the search for the 
optimum model algorithms and parameter settings that best represent the system of 






160 

interest. Discrepancy measures, experimental design, and analysis techniques were 

presented as tools for the calibration of IBSE simulation models. 

Based on the calibration and validation results for the model presented in this 
dissertation, several cautions should be made regarding predictive abilities and accuracy 
of any simulation model. As Box (1982: 117) noted, "all models are wrong; some models 
are useful." The difficulty then lies in determining which models are useful. Thus, 
adequate model validation is necessary for predictive accuracy. For example, in the model 
developed in this dissertation, final evaluation indicated that the model performed well 
using the water conditions under which it was developed. Although the simulated deer 
were sensitive to flood conditions, the sensitivity was not as high as expected when 
compared to the validation data that was collected during the flood. With the guidelines 
and detailed descriptions of the model development, verification, calibration, and 
validation of the model presented in this dissertation, the tools for building defensible 
models are now more approachable. 



n 



■» ■:'. 



APPENDIX A 
CALIBRATION DATA SET 



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168 



Table A.3. Annual habitat use (percentage of observations in each habitat) for white- 
tailed deer included in calibration data set. 



Deer ID 



Year^ 



WPR'' 



HPR 



TRE 



WSA 



Female 












89004 


1990 


58.9 


11.0 


17.8 


12.3 


89005 


1990 


46.6 


5.5 


26.0 


21.9 


89008 


1991 


56.1 


15.2 


12.1 


16.7 


89014 


1990 


37.3 


24.0 


18.7 


20.0 


89016 


1989 


69.1 


1.8 


12.7 


16.4 


89022 


1989 


57.1 


0.0 


28.6 


14.3 


89026 


1989 


19.6 


46.4 


26.8 


7.1 


89041 


1990 


23.1 


43.6 


30.8 


2.6 


89045 


1991 


58.2 


16.4 


20.9 


4.5 


89055 


1990 


31.6 


46.1 


19.7 


2.6 


89058 


1990 


25.3 


32.0 


32.0 


10.7 


89059 


1990 


88.1 


1.7 


3.4 


6.8 


89062 


1990 


5.2 


67.5 


18.2 


9.1 


89063 


1990 


29.8 


2.4 


58.3 


9.5 


90067 


1991 


75.9 


8.9 


6.3 


8.9 


90069 


1990 


79.2 


8.3 


5.6 


6.9 


90081 


1991 


80.3 


4.9 


1.6 


13.1 


90107 


1991 


42.6 


26.5 


22.1 


8.8 


90123 


1991 


83.6 


3.0 


1.5 


11.9 


90124 


1991 


67.2 


6.0 


22.4 


4.5 


90125 


1991 


44.4 


12.7 


17.5 


25.4 


90129 


1991 


73.1 


17.9 


4.5 


4.5 


90131 


1991 


85.3 


2.9 


0.0 


11.8 


90135 


1991 


80.6 


4.5 


10.4 


4.5 


90138 


1991 


24.3 


47.1 


4.3 


24.3 


90141 


1991 


90.5 


6.3 


1.6 


1.6 


Male 












89025 


1989 


32.7 


11.5 


28.8 


26.9 


89027 


1989 


11.1 


27.8 


38.9 


22.2 


. 89033 


1990 


5.4 


17.6 


50.0 


27.0 


89034 


1990 


20.0 


7.5 


48.8 


23.8 


■ 89046 


1991 


22.1 


19.1 


52.9 


5.9 


89052 


1990 


11.5 


46.2 


32.1 


10.3 



169 



Table A.3. 


- continued. 












Deer ID 


Year" 


WPR'' 


HPR 


TRE 


WSA 


Male 












■y , , - 


89060 


1990 


33.3 


14.7 


37.3 


14.7 




89061 


1990 


13.0 


3.9 


59.7 


23.4 




90078 


1990 


61.2 


10.0 


5.0 


23.8 




90091 


1990 


14.3 


15.6 


55.8 


14.3 




90109 


1990 


50.7 


13.7 


16.4 


19.2 




90128 


1991 


17.9 


43.3 


23.9 


14.9 




90130 


1991 


28.1 


9.4 


28.1 


34.4 



One year of data from each deer was randomly selected for inclusion into habitat 
selection analyses. 

'' WPR = wet prairie; HPR = herbaceous prairie; TRE = tree islands; WSA = 
willow/dense sawgrass. 



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173 



Table A.5. Mean hydrologic season habitat use (percentage of observations in each 
habitat) for white-tailed deer included in calibration data set. 



Deer ID 




Dry season 






Wet season 




J-'V.'WX XJ— ^ 


WPR^ 


HPR 


TRE 


WSA 


WPR 


HPR 


TRE 


WSA 


Female 


















89004 


41.7 


13.9 


25.0 


19.4 


70.3 


8.1 


10.8 


10.8 


89005 


52.2 


4.7 


16.4 


26.7 


56.8 


12.2 


24.3 


6.8 


89008 


53.0 


20.2 


14.2 


12.6 


52.9 


23.5 


8.8 


14.7 


89014 


33.3 


30.8 


23.1 


12.8 


37.6 


19.4 


22.4 


20.7 


89022 


55.4 


0.0 


23.8 


20.8 


65.8 


0.0 


20.5 


13.7 


89026 


22.5 


25.0 


40.0 


12.5 


15.0 


42.5 


32.5 


10.0 


89041 


16.6 


47.5 


29.4 


6.5 


30.6 


41.7 


27.8 


0.0 


89045 


63.9 


16.7 


15.3 


4.2 


46.6 


23.2 


21.1 


9.1 


89055 


59.0 


25.6 


11.5 


3.8 


35.1 


40.5 


24.3 


0.0 


89058 


40.1 


27.2 


26.1 


6.6 


36.6 


20.4 


26.6 


16.4 


89059 


92.3 


2.6 


0.0 


5.1 


83.3 


2.8 


11.1 


2.8 


89062 


14.7 


54.6 


16.0 


14.7 


4.1 


65.7 


16.5 


13.7 


89063 


32.1 


6.4 


47.8 


13.6 


27.3 


2.5 


55.6 


14.7 


90067 


77.8 


11.1 


4.9 


6.2 


67.9 


9.3 


8.6 


14.3 


90069 


81.1 


8.1 


8.1 


2.7 


75.0 


5.6 


5.6 


13.9 


90081 


86.2 


4.1 


1.4 


8.3 


91.7 


2.8 


2.8 


2.8 


90123 


83.8 


0.0 


2.7 


13.5 


73.9 


7.0 


5.7 


13.4 


90124 


69.4 


5.6 


25.0 


0.0 


71.2 


5.4 


16.1 


7.4 


90125 


41.7 


16.7 


19.4 


22.2 


51.4 


10.8 


21.6 


16.2 


90129 


75.0 


16.7 


5.6 


2.8 


75.8 


11.4 


7.4 


5.4 


90131 


88.9 


2.8 


0.0 


8.3 


81.7 


2.0 


0.0 


16.3 


90135 


77.8 


5.6 


11.1 


5.6 


88.2 


2.1 


7.6 


2.1 


90138 


23.7 


60.5 


2.6 


13.2 


27.3 


32.7 


8.2 


31.9 


90141 


87.5 


6.3 


3.1 


3.1 


88.5 


4.7 


5.4 


1.4 


Male 


















89033 


6.8 


25.7 


41.9 


25.7 


11.8 


21.7 


39.7 


26.9 


89034 


10.3 


13.3 


62.1 


14.3 


21.8 


13.8 


35.9 


28.4 


89046 


22.7 


20.0 


46.8 


10.6 


21.9 


17.4 


37.6 


23.2 


89052 


12.9 


43.1 


33.4 


10.6 


12.6 


48.1 


27.7 


11.5 


89060 


45.1 


13.1 


26.1 


15.7 


15.1 


17.4 


50.9 


16.6 


89061 


21.2 


12.0 


43.1 


23.7 


9.7 


2.8 


65.3 


22.2 



174 



Table A.5. - ( 


continued. 
















Deer ID 




Dry season 






Wet season 




WPR 


HPR 


TRE 


WSA 


WPR 


HPR 


TRE 


WSA 


Male 


















90078 


57.3 


10.1 


13.3 


19.4 


62.2 


8.1 


10.8 


18.9 


90091 


27.4 


12.3 


43.8 


16.5 


3.2 


15.6 


59.8 


21.4 


90109 


41.2 


18.8 


22.8 


17.2 


47.4 


18.4 


23.7 


10.5 


90128 


27.8 


50.0 


13.9 


8.3 


10.6 


27.8 


39.1 


22.5 


90130 


43.2 


8.1 


16.2 


32.4 


11.1 


2.8 


36.1 


50.0 



" WPR = wet prairie; HPR 
willow/dense sawgrass 



APPENDIX B 

DESCIOPTION OF PARAMETER SYMBOLS USED IN THE 

CALIBRATION EXPERIMENTS 



Symbol Factor description 



X 

ML 

MLh 

MLp 

STEP 

STEPd 

STEP 



w 



a 
P 
Y 

■^WPR 
^HPR 
^TRE 
AwSA 
■'^TWS 

■'\:ys 

■^PIN 
AcYP 

A, 



^MAN 



LD 



WEIGHT 



LD, 



PROB 



MLr 

An 



Maximum affinity for homing beacon 

Distance (m) from homing beacon at which affinity is ^ 

Relative affinity for previously visited pixels 

Memory length (5-day intervals) for homing beacon and pixel memory 

Memory length (5-day intervals) for homing beacon 

Memory length (5-day intervals) for pixel memory 

Nimiber of moves per 5-day interval 

Number of moves per 5 -day interval in the dry season 

Number of moves per 5-day interval in the wet season 

Relative affinity for water depths < p cm 

Water depth (cm) below which relative affinity is a 

Water depth (cm) above which relative affinity is 1 

Relative affinity for wet prairie 

Relative affinity for herbaceous prairie 

Relative affinity for tree islands 

Relative affinity for willow/dense sawgrass 

Relative affinity for tree islands/willow/dense sawgrass 

Relative affinity for cypress swamp and prairie 

Relative affinity for pine 

Relative affinity for cypress/pine 

Relative affinity for mangrove 

Weight of habitat and water affinity for pixels farther away than one 

pixel. Weight of habitat and water affmity for neighboring 

pixels is 1-LDwEiGHT- 
Probability of habitat and water values farther away than one pixel 

being included in the movement decision 

MLrXSTEP is the length of short term memory (pixels with a relative 

affmity of Ar< 1.0) 
Relative affinity for pixels visited in the past MLp x STEP moves 



175 



, ''v *', 



APPENDIX C 
SUMMARY OF CALIBRATION EXPERIMENTS FOR FEMALES 



H-' '. '/y- . '-• ■"■ I i 






Table C.l. Summary of calibration experiment 1 for females. 



Algorithm changes Movement algorithms were as described in text (Section 4.2) 

except that water depth is not included in the movement decision. 
Habitat accounted for 50% of the movement decision. 



Experiment design 2^' fractional factorial with 32 EUs, all main effects and first- 
order interactions were estimable. Simulations were run for 15 
years. 

Fixed parameters were Awpr=10, Ahpr=20, AcYp=Ap^=10, 



Analysis results 



^ 



•• • i 



«nv«' 



^MAN~l- 



Factor 



Low 



High 



X 

STEP 

ML 

A 

^TRE.WSA 



3 
750 

4 

100 
12 
30 



5 
1750 

12 
300 

24 

50 



Experimental bum-in was estimated at 4 years, so data from the 
5* year of simulation were analyzed. 

All average home range sizes were larger than those observed in 
the field. Discrepancies were significantly smaller with smaller 4), 
smaller ^l, larger X, smaller STEP, and larger At-re,wsa- Distance 
between consecutive centers ranged from very close to the 
observed average to more than three times the observed average. 
Discrepancies were reduced with larger cj), smaller \i, and a longer 
ML. Average distance between consecutive locations ranged 
from 458 m to 847 m, encompassing the observed value of 686 
m. Discrepancies were significantly smaller with smaller [i and 
larger STEP. On average, simulated deer were observed in tree 
islands and herbaceous prairie more and wet prairie less than 
observed deer, indicating a need for ftirther evaluation of habitat 
relative affinities. An increase in ML and a decrease in STEP 
caused a decrease in the chi-square discrepancy measure for 
habitat. 

The next experiment will keep current experimental factors the 
same and add relative affinities for the other habitats. 



177 



I lA'JV 



178 



Table C.2. Summary of calibration experiment 2 for females- 
Algorithm changes None. 



Experiment design 2""* fractional factorial with 32 EUs, all main effects were 
estimable. Simulations were run for 15 years. 
Fixed parameters were AwpR=10. 

Factor Low High 



Analysis results 



* 


3 


5 


t» 


750 


1750 


X 


4 


12 


STEP 


100 


300 


ML 


12 


24 


•^HPR 


20 


30 


"^TRE 


20 


50 


■^WSA 


30 


50 


■^CYS 


5 


15 


■^PIN 


5 


15 


Aman 


1 


10 



Experimental bum-in was estimated at 5 years, so data from the 
6"" year of simulation were analyzed. 

Discrepancies for average home range size were significantly 
smaller with smaller (}), smaller \x, larger k, smaller STEP, and 
larger Atrj,. Discrepancies for distance between consecutive 
centers were reduced with larger <j), smaller |i, longer ML, and 
larger STEP. Discrepancies for average distance between 
consecutive radio-locations were significantly smaller with larger 
STEP. Discrepancies for habitat use were significantly smaller 
with smaller Ahp^; however, average percent time observed in 
tree islands was much larger then observed in the field. Mean 
discrepancy (MD) was significantly reduced with larger 4), 
smaller \i, and longer ML, and larger A^r^. 

For the subsequent simulation experiment, <j) was increased, and 
Ahpr, Atre, and A^ja. and A^^ were reduced. A^vs and Apj^ 
were combined to become A^yp in future experiments. 



179 



Table C.3. Summary of calibration experiment 3 for females- 
Algorithm changes None. 



Experiment design 2"'-' fractional factorial with 32 EUs, all main effects were 
estimable. Simulations were run for 15 years. 
Fixed parameters were Aw,pR=10. 

Factor Low High 



4) 


4 


6 


V^ 


750 


1750 


k 


4 


12 


STEP 


100 


300 


ML 


12 


24 


^HPR 


10 


20 


^TRE 


20 


40 


•^WSA 


20 


40 


■'^CYP 


5 


10 


. A^,^^, 


5 


10 



Analysis results 



Based on experimental bum-in time, year 8 data were analyzed. 
The largest reduction in mean home range size discrepancy was 
seen with smaller \i and smaller STEP. Discrepancies for distance 
between consecutive centers were most reduced with longer ML. 
Discrepancies for mean distance between consecutive radio- 
locations were most reduced with larger STEP. Overall, habitat- 
use patterns were reduced relative to the previous experiment, 
and discrepancies were most reduced with smaller STEP. MD 
was reduced with smaller |i and longer ML. 

For the subsequent simulation experiment, \i was reduced and 
ML was increased. 



180 



Table C.4. Summary of calibration experiment 4 for females. 
Algorithm changes None. 



Experiment design 2'°'' fractional factorial with 32 EUs, all main effects were 
estimable. Simulations were run for 15 years. 

,=10. 
Factor Low High 



Analysis results 



Fixed parameters were A^pr- 



d) 


4 


6 


1^ 


500 


1000 


A 


4 


12 


STEP 


100 


300 


ML 


24 


48 


^HPR 


10 


20 


Atre 


20 


40 


AwSA 


20 


40 


■^CYP 


5 


10 


^MAN 


5 


10 



Based on experimental bum-in time, year 8 data were analyzed. 
The largest reduction in mean home range size discrepancy was 
seen with larger ^, smaller |i and smaller STEP. Discrepancies 
for distance between consecutive centers were most reduced with 
larger STEP and longer ML. Discrepancies for mean distance 
between consecutive radio-locations were most reduced with 
larger STEP. Discrepancies in habitat use were most reduced 
with smaller A„pR. MD was minimized with larger ({), smaller \i, 
larger STEP, and smaller Ahpr. 

For the subsequent simulation experiment, separate memory 
lengths were used for the homing beacon and the pixel memory 
algorithms. Ahpr was reduced. 



181 



Table C.5. Summary of calibration experiment 5 for females. 

Algorithm changes The length of the moving window for the homing beacon 



algorithm and the length of the moving window for the pixel 
memory algorithm were programmed to be separate parameters 
the simulation. 



Experiment design 2 



11-6 



estimable. Simulations were run for 15 years. 
Fixed parameters were AwpR=10. 

Factor Low 



High 





4) 


4 


6 




^ 


500 


1000 




X 


4 


12 




STEP 


100 


300 


^; ' r ■■-.', ^ 


MLh 


24 


48 




MLp 


6 


36 


■i ■■ , i • 


^HPR 


10 


15 




-^TRE 


20 


40 


^ ■ > f--«. ;: J -' ■', • f ' 


■^WSA 


20 


40 




^YP 


5 


10 




'^MAN 


5 


10 


Analysis results Based on experir 


nental bum-in time, 


year 8 da 


ita were analvzed. 



The largest decrease in mean home range size discrepancy was 
seen with smaller \i and smaller STEP. Discrepancies for distance 
between consecutive centers were most reduced with larger STEP 
and longer ML^. Discrepancies for mean distance between 
consecutive radio-locations were reduced with larger STEP. 
Discrepancies in habitat use were reduced most with smaller 
AjRE- MD was reduced most with larger 4), smaller \i, larger 
STEP, smaller A^pR, and longer MI^. 

For the subsequent simulation experiment, the water depth 
algorithm was introduced. Also, 4), STEP, and MI^ were 
increased, and Atpp was decreased. 



182 



Table C.6. Summary of calibration experiment 6 for females. 



Algorithm changes The water depth algorithm, as discussed in Section 4.2.2.b. was 

introduced and weighted as discussed in Section 4.2.2.d. 

Experiment design 2 "'" fractional factorial with 32 EUs, all main effects were 
estimable. Simulations were run for 15 years. 

R=10. 

Factor Low High 



Fixed parameters were A^p^- 







♦ 


5 


7 






1* 


500 


1000 






A 


4 


12 






a 


10 


30 






P 


10 


30 






Y 


40 


60 






STEP 


200 


400 






ML„ 


36 


60 






MLp 


6 


36 






■'^HPR 


10 


15 






Aire 


15 


30 






■^WSA 


20 


40 






A:yp 


5 


10 






'^MAN 


5 


10 


Analysis results 


Based on experin 


lental bum-in tim 


e, year 9 da 


ta were analv^ed 



The largest reduction in mean home range size discrepancy was 
seen with smaller \i, smaller MLp, and larger L Discrepancies for 
distance between consecutive centers were not affected by any 
experimental factors and appeared to be nearing zero. 
Discrepancies for mean distance between consecutive radio- 
locations were slightly reduced with smaller STEP. Discrepancies 
in habitat use were most reduced with smaller p. MD was 
minimized with smaller |i. 

For the next experiment, \i and MLp were reduced. 



183 



Table C.7. Summary of calibration experiment 7 for females- 
Algorithm changes None. 



Experiment design 2"'" fractional factorial with 32 EUs, all main effects were 
estimable. Simulations were run for 15 years. 
Fixed parameters were Awpr=10. 

Factor Low High 

4) 



k 
a 



Y 
STEP 

MLh 
MLp 

^HPR 
^TRE 
■^WSA 
•^CYP 

-'^MAN 



5 


7 


250 


750 


4 


12 


10 


30 


10 


30 


40 


60 


200 


400 


36 


60 


3 


12 


10 


15 


15 


30 


20 


40 


5 


Id 


5 


10 



Analysis results Based on experimental bum-in time, year 8 data were analyzed. 
The largest reduction in mean home range size discrepancy was 
seen with larger ^, smaller [i, smaller MLp, and larger A. 
Discrepancies for distance between consecutive centers were 
reduced with shorter MLh. Discrepancies for mean distance 
between consecutive radio-locations were slightly reduced with 
larger STEP. Discrepancies in habitat use were most reduced 
with larger A^sa and larger A^an- MD was minimized with larger 

•'^WSA- 

For the next experiment, A^sa was increased, Acyp was fixed at 
^ ^ 7.5, and A^an was fixed at 10. Simulated deer will make more 
' steps in the dry winter than in the wet summer. 



184 



Table C.8. Summary of calibration experiment 8 for females. 

Algorithm changes Individuals moved fewer steps in the wet season than in the dry 
season by having probability <1 of making a step in each 
movement iteration. 



Experiment design 2'^'' fractional factorial with 64 EUs, all main effects and some 
interactions were estimable. Simulations were run for 15 years. 
Fixed parameters were AwpR=10, AcYP=7.5, A^,^=10. 
Factor Low High 



<t> 


5 


7 


\^ 


250 


750 


X 


4 


12 


a 


10 


30 


P 


10 


30 


Y 


40 


60 


STEPd 


400 


500 


STEPw 


STEPd-200 


STEPd- 100 


ML„ 


36 


60 


MLp 


3 


12 


Ahpr 


10 


15 


■^TRE 


15 


30 


AwSA 


20 


40 



Analysis results 



Based on experimental bum-in time, year 9 data were analyzed. 

The largest reduction in mean home range size discrepancy was 
seen with larger ^, smaller \i, smaller MLp, and larger A,. 
Discrepancies for distance between consecutive centers were 
reduced with shorter ML„. Discrepancies for mean distance 
between locations were not affected by any experimental factors 
and appeared to be nearing zero. Discrepancies in habitat use 
were most reduced with larger A^re. MD was minimized with 
smaller \i, shorter MLh, and larger Aj^. 

For the next experiment, \i and MLh were reduced and Atr^ was 
increased. 



■'- , f '■' 



185 



Table C.9. Summary of calibration experiment 9 for females- 
Algorithm changes None. 



Experiment design 2 '^"^ fractional factorial with 64 EUs, all main effects and some 
interactions were estimable. Simulations were run for 15 years. 
Fixed parameters were Awpr=10, Acyp=7.5, Aman=10. 
Factor Low High 



<^ 


5 


7 


J* 





500 


;i 


4 


12 


a 


10 


30 


P 


10 


30 


Y 


40 


60 


STEPd 


400 


500 


STEPw 


STEPd-200 


STEPd-100 


ML„ 


24 


48 


MLp 


3 


12 


■^HPR 


10 


15 


■'^TRE 


20 


40 


_ ^WSA 


30 


50 



Analysis results Based on experimental bum-in time, year 9 data were analyzed. 
The largest reduction in mean home range size discrepancy was 
^ ., . seen with larger <J), smaller \i, larger X and smaller MLp. 

Discrepancies for distance between consecutive centers were 
reduced with longer MLh. Discrepancies for mean distance 
between locations were reduced with longer MLp. Discrepancies 
:', .. / ' ^-f in habitat use were not significantly affected by any experimental 

• ' factors. MD was minimized with smaller n, larger A,, shorter 
MLh, and larger Atre. Visual assessment indicated that some 
individuals were still getting 'stranded' in the prairie or getting 
'stuck' on a tree island. 

For the next experiment, an algorithm incorporating habitat and 
water affinities farther than one pixel from current location was 
incorporated. 




186 



Table CIO. Summary of calibration experiment 10 for females. 

Algorithm changes Introduced algorithm incorporating habitat and water affinities 
farther then one pixel from current location (Fig. 4.10). 



Experiment design 2"*-' fractional factorial with 32 EUs, all main effects were 
explored. Simulations were run for 1 5 years. 
Fixed parameters were Awpr=10, Acyp=7.5, Aman=10. 
Factor Low High 






Analysis results 



4> 


5 


7 


f* 





500 


X 


4 


12 


a 


10 


30 


P 


10 


30 


y 


40 


60 


STEPd 


400 


500 


STEPw 


STEPd-200 


STEPd-IOO 


MLh 


24 


48 


MLp 


3 


12 


A 


10 


15 


■'^TRE 


20 


40 


-^WSA 


30 


50 


^^WEIGHT 


0.2 


0.4 



Based on experimental bum-in time, year 9 data were analyzed. 
Relative to experiment 9 (Table C.9), home range sizes were 
larger, percent observations in WPR decreased, and percent 
observations in TRE increased, indicating a shift away from the 
calibration data. Visual assessment indicated deer were more 
likely to find and utilize nearby tree islands. The largest reduction 
in mean home range size discrepancy was seen with larger <(), 
smaller ji, larger X and smaller MLp. Discrepancies for distance 
between consecutive centers were not significantly affected by 
any experimental factors. Discrepancies for mean distance 
between locations were reduced with smaller X and longer MLp. 
Discrepancies in habitat use were minimized with smaller A^re. 
MD was minimized with larger (j). 

For the next experiment, the habitat and water affinity algorithms 
were modified further; (j, was fixed at m, and several values of 
several experimental factors (model parameters) were adjusted. 



187 



Table C.ll. Summary of calibration experiment 1 1 for females. 

Algorithm changes Probability of habitat and water values farther away than one 

pixel being included in the movement decision is either 0.5 or 1.0 
for each movement step. 

Experiment design 2'"' fractional factorial with 32 EUs, all main effects were 
explored. Simulations were run for 15 years. 
Fixed parameters were \x=0, Awpr=10, Acyp=7.5, Aman=10. 
Factor Low High 



Analysis results 



<t> 


6 


8 


X 


6 


12 


a 


10 


30 


P 


10 


30 


Y 


40 


60 


STEPd 


400 


500 


STEPw 


STEPd-200 


STEPp-lOO 


MLh 


20 


28 


MLp 


3 


12 


•'^HPR 


10 


15 


Atre 


15 


30 


■'^WSA 


30 


40 


^^WEIGHT 


0.2 


0.4 


^^PROB 


0.5 


1.0 



Based on experimental bum-in time, year 9 data were analyzed. 
The largest reduction in mean home range size discrepancy was 
seen with larger ^, larger X and smaller MLp. Discrepancies for 
distance between consecutive centers were significantly reduced 
with longer MLh. Discrepancies for mean distance between 
locations were reduced with longer MLp. Discrepancies in habitat 
use were not significantly affected by any experimental factors. 
MD was minimized with larger STEP. 

For the next experiment, the homing beacon algorithm was 
modified. 




188 



Table C.12. Summary of calibration experiment 12 for females. 



Algorithm changes Homing beacon algorithm was modified from Fig. 4.7 to Fig 
4.11. 



Experiment design 2''*"' fractional factorial with 32 EUs, all main effects were 
explored. Simulations were run for 15 years. 
Fixed parameters were [1=0, Awpr=10, Acyp=7.5, Aman=10- 
Factor Low High 



Analysis results 



* 


6 


8 


X 


6 


12 


a 


10 


30 


P 


10 


30 


Y 


40 


60 


STEPd 


400 


500 


STEPw 


STEPd-200 


STEPd-100 


MLh 


20 


28 


MLp 


3 


12 


Ahpr 


10 


15 


■^TRE 


15 


30 


-^WSA 


30 


40 


LDwEIGHT 


0.2 


0.4 


^^PROB 


0.5 


l.O 



Based on experimental bum-in time, year 9 data were analyzed. 
Changing the homing beacon algorithm had a large impact on the 
home range size, as the mean home range area was 1 1 1 ha for the 
simulated deer (compared to means of 271 ha for the observed 
females and 356 ha for the simulated deer in experiment 1 1). Any 
changes in the discrepancy measures due to experimental factors 
were relatively small. 

For the next experiment, ^ was reduced and \i was included as a 
factor with levels of O and 1000 m. 



189 



Table C.13. Summary of calibration experiment 13 for females. 

Algorithm changes None. 

Experiment design l'^"'" fractional factorial with 32 EUs, all main effects were 
explored. Simulations were run for 15 years. 
Fixed parameters were Awpr=10, Acyp=7.5, Aman=10- 
Factor Low High 



* 


3 


5 


1* 





1000 


X 


6 


12 


a 


10 


30 


P 


10 


30 


Y 


40 


60 


STEPd 


400 


500 


STEPw 


STEPd-200 


STEPd-100 


MLh 


20 


28 


MLp 


3 


12 


°HPR 


10 


15 


"tre 


15 


30 


PwSA 


30 


40 


^^WEIGHT 


0.2 


0.4 


^^PROB 


0.5 


l.O 



Analysis results Based on experimental bum-in time, year 9 data were analyzed. 
The largest reduction in mean home range size discrepancy was 
seen with larger n. Discrepancies for distance between 
consecutive centers were significantly reduced with larger \i. 
Discrepancies for mean distance between locations were reduced 
with smaller 4), larger \i, and longer MLp. Discrepancies in habitat 
use were not significantly affected by any experimental factors. 
MD was minimized with larger \i. 

For the next experiment, levels of \i were set closer to 1000 m. 



190 



Table C.14. Summary of calibration experiment 14 for females- 
Algorithm changes None. 



Experiment design l'^"'" fractional factorial with 32 EUs, all main effects were 
explored. Simulations were run for 15 years. 
Fixed parameters were Awpr=10, Acyp=7.5, Aman=10. 
Factor Low High 



* 


3 


5 


1* 


750 


1250 


X 


6 


12 


a 


10 


30 


P 


10 


n 


Y 


40 


m 


STEPd 


400 


500 


STEPw 


STEPd-200 


STEPd-100 


MLh 


20 


28 


MLp 


3 


12 


Ahpr 


10 


15 


"^TRE 


15 


3© 


■^WSA 


30 


40 


^^WEIGHT 


0.2 


0-4 


^^PROB 


0.5 


1.0 



Analysis results Based on experimental bum-in time, year 9 data were analyzed. 
Based on the mean outcomes and the discrepancy measures, the 
,^ . current model parameterization appears to be getting close to the 

' ideal on an annual basis, with respect to the calibration data. The 
largest reduction in mean home range size discrepancy was seen 
with larger (|) and smaller |i. Discrepancies for distance between 
consecutive centers were significantly reduced with larger \i. 
Discrepancies for mean distance between locations were reduced 
with smaller (j), larger \i, and longer MLp. Discrepancies in habitat 
use were most reduced with smaller Ahpr. MD also was 
minimized with smaller A^pr. 

For the next experiment, several model parameters were held 
fixed at one value, and other parameter values were adjusted. 



191 



Table CIS. Summary of calibration experiment 15 for females. 
Algorithm changes None. 



Experiment design 2""* fractional factorial with 32 EUs, all main effects were 
explored. Simulations were run for 15 years. 

Fixed parameters were y=40, Awpr=10, Ahpr=10, Awsa=35, 
AcYp=7.5, A^,^=10, LDpROB=10. 

Factor Low High 



Analysis results 



♦ 


2 


4 


H 


750 


1250 


X 


10 


40 


a 


10 


30 


P 


10 


30 


STEPd 


400 


500 


STEPw 


STEPd-100 


STEPi, 


MLh 


18 


24 


MLp 


3 


12 


■^TRE 


15 


25 


^^WEIGHT 


0.2 


0.4 



Based on experimental bum-in time, year 9 data were analyzed. 
The largest reduction in mean home range size discrepancy was 
seen with larger ^ and smaller \i. Discrepancies for distance 
between consecutive centers were significantly reduced with 
larger (j). Discrepancies for mean distance between locations were 
not significantly affected by any experimental factors and the 
mean discrepancy was <100 m. Discrepancies in habitat use not 
significantly affected by any experimental factors. MD was 
minimized with larger cj). 

Visual examination of randomly selected movement paths 
indicated that simulated deer selected the 'best' available habitat 
(as determined by the relative habitat affinities and water depths) 
during the small-scale movement step a large percentage of the 
time. Because it was unlikely that deer would always select the 
best habitat at all times, the habitat and water depth weights for 
the second stage of the movement were adjusted in the next 
experiment. Also, some parameter values were adjusted. 



192 



Table C.16. Summary of calibration experiment 16 for females. 

Algorithm changes Probabilities of moving to each 20-m pixel based on habitat and 
water depth were calculated from relative affinities, and the 
probabilities of moving to each cell were now calculated as: 



^; = 



■p^j 



1 



1 1 

+ — X — 
2 9 



where/? \j and/? \j were the probabilities of moving to the 20-m 
pixely based on habitat and water depth, respectively. The deer 
selected a 20-m pixel based on a random draw from the 
multinomial distribution (ti'i, ti',, tt'j, . . . , %\). 



Experiment design 2*-^ fi-actional factorial with 1 6 EUs, all main effects were 
explored. Simulations were run for 1 5 years. 
Fixed parameters were ti=1000, X=30, STEPd=STEPw=400, 
MLh=21, Awpr=10, Acyp=7.5, Aman=10, LDweight=0.2, 



i / 



Analysis results 



'^^PROB 1 •^• 



Factor 



Low 



High 



a 
Y 
P 

MLp 

^TRE 



2 

10 

40 

10 

3 

10 

15 

30 



4 

30 
tiO 
301 

la 

15 
2S 

40 



Based on experimental bum-in time, year 9 data were analyzed. 
The largest reduction in mean home range size discrepancy was 
seen with larger ^. Discrepancies for distance between 
consecutive centers were significantly reduced with larger (J). 
Discrepancies for mean distance between locations were reduced 
with smaller 4). Discrepancies in habitat use not significantly 
affected by any experimental factors. MD was most minimized 
with larger 4). 

Because the change in the algorithm did not appreciably impact 
the simulation outcomes, the original weights for 20-m pixel 
selection were used in future simulations. Future experiments 
will focus on reducing bum-in time and reducing likelihood of 
deer moving to a tree island and using it exclusively. Several 
series of experiments were conducted to develop the algorithm 
changes in the following experiment (Table C.17) that were not 
reported in this appendix. 



193 



Table C.17. Summary of final calibration experiment for females. 

Algorithm changes To reduce bum-in time for home range size, the homing beacon 



was 10% of the movement decision at the start of the simulation 
and was increased to 25% when the simulation reached the length 
of the memory (as before). 

Since reducing STEP in the wet season did not produce the 
desired seasonal changes, this approach was abandoned. Instead, 
4) was decreased by 1 .0 if the water depth at P-34 <0 cm (to 
simulate the deer traveling more to find sufficient forage). 
To minimize the frequency of deer finding a preferred location 
and staying there (i.e., staying on a tree island), deer had a very 
low affinity for pixels visited in the immediate past. 



Experiment design 2^ fractional factorial with 4 replications of each factor 

combination; all interactions were estimable. Simulations were 
run for 10 years. 

Fixed parameters were |i= 1 000, <t)=4, X=5, A,r=0.5, MLh=24, 
MLp=6, a=20, P=10, y=40, A^p,=10, A„pR=10, Awsa=40, 
AcYp=7.5, Aman=10, LDweight=0.2, LDpROB=10. 



Factor 



Low 



High 



STEP 

MLr 

A. 



^TRE 



200 
0.2 

25 



400 
0.4 

35 



Analysis results 



Based on experimental bum-in time, year 5 data were analyzed. 
Home range size discrepancy was reduced with smaller STEP 
and shorter MLr. Discrepancies for distance between consecutive 
centers were significantly reduced with larger STEP. 
Discrepancies for mean distance between locations were reduced 
with smaller STEP and shorter MLr. Discrepancies in habitat use 
were minimized with larger At-re. 

Final model settings were determined based on results from this 
experiment (see Secfion 4.4). 



(T ; ""t -••T.HW^l^.!"ff.."'-"i.v 



APPENDIX D 
SUMMARY OF CALIBRATION EXPERIMENTS FOR MALES 



Table D.l. Summary of calibration experiment 1 for males. 



Algorithm changes 



All algorithms were the same as those for the final model for 
females except the homing beacon. Since males tend to travel 
more during rut, <() was reduced by 1 during rut (July, August, and 
September) and by V2 just before (June) and just after (October) 
rut. 



Experiment design r fi-actional factorial with 4 replications of each factor 



Analysis results 



combination. Simulations were run for 10 years. 
Fixed parameters were n=500, (|)=4, X=5, A.r=0.5, MLh=24, 
MLp=6, a=10, P=30, y=60, Awpr=10, Ahpr=10, Acyp=7.5, 
Aman=10, LD^eight=0.2, LDpROB=1.0, MLr=0.2. 

Factor Low High 



STEP 



^TWS 



200 
50 



300 
100 



Based on experimental bum-in time, year 5 data were analyzed. 
Home range size discrepancy was reduced with larger A^ws- 
Discrepancies for distance between consecutive centers were not 
significantly reduced by either factor. Discrepancies for mean 
distance between locations were reduced with larger STEP. 
Discrepancies in habitat use were minimized with larger Aj^s- 
MD was minimized with larger STEP and Ayws 
Overall, habitat-use patterns of the simulated males did not 
correspond well with those observed in the field. The weight of 
habitat affinity in the movement decision was increased in an 
attempt to improve habitat use patterns. 



195 



196 



Table D.2. Summary of calibration experiment 2 for males. 

Algorithm changes Habitat affinity was made to have more impact on the 60-m 



Experiment design 



movement stage by altering the weighted average for calculation 
of the probability of moving to pixely (j = 1,2,3, ... , 9): 
Hj = 0.35 X ;, ^,.^, + 0. 15 X p ^^,^^ + 0.25 x p ,„„,„^ ,,,,„„ 

+ 0.25 X n , 

-r Pixel memory 



2' fractional factorial with 4 replications of each factor 
combination. Simulations were run for 10 years. 
Fixed parameters were ti=500, <j)=4, X=5, Ar=0.5, MLh=24, 
MLp=6, a=10, p=30, y=60, Av,pr=10, A„pR=10, Acyp=7.5, 



Amak=10, LD 



WEIGHT ^-2, LDpROB 

Factor 



rl.0,MLR=0.2. 
Low High 



STEP 

Ajws 



200 
50 



300 
100 



Analysis results 



Several EUs never reached a steady state (i.e., bum-in not 
completed). Time plots of the outcome variables indicated 
percentage of observations in tree islands increased and 
percentage of observations in wet prairie decreased throughout 
the 10 year simulation for these runs. 
No further analyses were performed. 

In the next experiment, the algorithm change (described above) 
was reversed, and the weight of the 'long-distance' habitat and 
water affinities were increased. 



197 



Table D.3. Summary of calibration experiment 3 for males. 

Algorithm changes Changed weighted average for calculation of the probability of 
moving to pixel/ (/• = 1, 2, 3, . . . , 9) back to the original (i.e., 
four equally weighted factors). Increased MLr to 0.5. 



Experiment design 



Analysis results 



2^ fractional factorial with 4 replications of each factor 
combination. Simulations were run for 10 years. 
Fixed parameters were n=500, 4)=4, A.=5, A,r=0.5, MLh=24, 
MLp=6, a=10, p=30, y=60, AwpR=10, Ahpr=10, Acyp=7.5, 
Aman=10, LDwe,ght=0.2, LDpROB=1.0, MLr=0.5. 

Factor Low High 



STEP 



^TWS 



200 
50 



300 
100 



Experimental bum-in time was still an issue because four of the 
sixteen EUs did not reach a steady-state by year 5; however the 
problem was lessened relative to the previous experiment. 
Analyses were conducted using year 5 data to indicate a direction 
for further experimentation. 

Home range size discrepancy was reduced with larger Atws- 
Discrepancies for distance between consecutive centers were not 
significantly reduced by either factor. Discrepancies for mean 
distance between locations were reduced with smaller A^ws and 
larger STEP. Discrepancies in habitat use were minimized with 
larger A^ws; however, the habitat use of the simulated deer 
deviated greatly from habitat use of the observed males (i.e., 
simulated deer were observed more frequently in the prairies and 
less frequently in the wooded areas than observed males). MD 
was minimized with larger STEP. 

LDwFip.HT was increased in the next experiment. 



198 



Table D.4. Summary of calibration experiment 4 for males. 

Algorithm changes Increased LD^eight to 0.4 for both the habitat algorithm and the 
water algorithm for the 60-m stage. 



Experiment design 2^ fractional factorial with 4 replications of each factor 
combination. Simulations were run for 10 years. 
Fixed parameters were |j,=500, (j)=4, X=5, A.r=0.5, MLh=24, 
MLp=6, a=10, p=30, Y=60, AwpR=10, Ahpr=10, AcYP=7.5, 
Aman=10, LDweioht=0.4, LDpROB=1.0, MLr=0.5. 

Factor Low High 



Analysis results 



STEP 

A. 



^TWS 



200 
50 



300 
100 



Simulation bum-in remained an issue because two of the sixteen 
EUs did not reach a steady-state by year 5; however, year 5 data 
were analyzed to guide further experimentation with the focus on 
further optimization of habitat use. 

With At-ws = 100, habitat-use patterns approached those observed 
in the field, but simulated deer still were observed more 
frequently in the prairies and less frequently in the wooded areas 
than observed males. 

In the next experiment, (|) was reduced and several changes were 
made to the initialization of the simulation. 



199 



Table D.S. Summary of calibration experiment 5 for males. 



Algorithm changes In previous experiments, starting locations were the same as 

those used for female experiments. Since observed males were 
more selective in home range selection, the initialization routine 
was altered. Starting locations for deer were randomly located 
within the 1.5 km boundary of the edge of the habitat map. For 
the first five months of the simulation, the probability of moving 
to pixel/ (/ = 1, 2, 3, . . . , 9; was calculated as 

■^j = 0.45 X p ^^^.,^, + 0.45 X ;, ^^^^ + 0.05 x p ,„„,„^,^^^„„ 

+ 0.05 X n . , 

r" pixel memory 

After five months, the above probability was calculated using 
equal weights for all four factors (as in previous simulations). 
This would allow the deer to have a better opportunity to find 
suitable home range sites. 



Experiment design 2^ fi-actional factorial with 4 replications of each factor 
combination. Simulations were run for 10 years. 
Fixed parameters were |i=500, <^=3, X=5, Ar=0.5, MLh=24, 
MLp=6, a=10, P=30, y=60, A^p,=10, Ahpr=10, Acyp=7.5, 



Analysis results 



Aman=10, LDwe,ght=0.4, LDp„oB=10, MLp=0.5 



Factor 



Low 



High 



STEP 

Atws 



200 
50 



300 
100 



Based on experimental bum-in time, year 5 data were analyzed. 
Home range size discrepancy was reduced with larger A^-ws- 
Discrepancies for distance between consecutive centers were not 
significantly reduced by either factor. Discrepancies for mean 
distance between locations were reduced with larger STEP. 
Discrepancies in habitat use were not significantly reduced by 
either factor. However, the mean percentage of observations in 
each habitat for the simulated deer was closer to those observed 
in the field than mean outcomes from the 4"" experiment. Within 
this experiment, large A^^^ produced mean percentages of 
observations in each habitat closer to the observed data. MD was 
minimized with larger A^ws and larger STEP. 

STEP was fixed at 250. (j) and Ahpr were included as a factors in 
the next experiment. 









200 



Table D.6. Summary of calibration experiment 6 for males. 

Algorithm changes None. 

Experiment design 1} fractional factorial with 4 replications of each factor 

combination. Simulations were run for 10 years. 
4 /■ . ■ ' j Fixed parameters were n=500, A=5, Xr=0.5, MLh=24, MLp=6, 

STEP=250, a=10, p=30, Y=60, AwpR=10, A„pR=10, Acyp=7.5, 
-' , ' . . Aman=10, LDwe,ght=0.4, LDpROB=l 0, MLr=0.5. 

Factor Low High 



>... 'w 



Analysis results 



4) 



^HPR 



^TWS 



3 

20 
60 



3.5 
40 
90 



Based on experimental bum-in time, year 4 data were analyzed. 
Home range size discrepancies and discrepancies for distance 
between consecutive centers were reduced with larger (j). 
Discrepancies for mean distance between locations were reduced 
with smaller (j). Discrepancies in habitat use not significantly 
reduced by any factor. When mean percentages of observations in 
each habitat for the simulated deer were evaluated, Ahpr=20 and 
Ajws=90 produced outcomes more similar to those observed in 
the field; however, mean percentage of observations in 
willow/dense sawgrass ( 1 0%) was much lower than expected 
based on the field data (18%). MD was minimized with larger 
A-rws and larger STEP. 

Seasonal shifts also were analyzed. Changes similar to those seen 
in the field were observed for home range size and distance 
between consecutive locations, but there was little shift in season 
habitat use patterns. 

AwsA was increased relative to k-^^. Algorithm changes to 
promote seasonal shifts in habitat use were made. 



201 



Table D.7. Summary of calibration experiment 7 for males. 

Algorithm changes <j) was reduced by 1 .5 during rut (July, August, and September) 
and by 0.75 just before (June) and just after (October) rut. 



Experiment design 



Analysis results 



2' fractional factorial with 4 replications of each factor 
combination. Simulations were run for 10 years. 

Fixed parameters were (1)=3.5, n=500, X=5, Ar=0.5, MLh=24, 
MLp=6, STEP=250, a=10, p=30, y=60, Awpr=10, Acyp=7.5, 
Aman=10, LDwe,ght=0.4, LDpROB=l-0, MLr=0.5. 

Factor Low High 



l <trf- 



^HPR 



^TRE 



'■WSA 



20 
70 
80 



30 
90 
100 



Based on experimental bum-in time, year 5 data were analyzed. 
Home range size discrepancies were reduced with larger Atr^ . 
Discrepancies for distance between consecutive home range 
centers, mean distance between locations, and habitat use were 
not significantly reduced by any factor. MD was minimized with 
larger Aj^. Overall, simulated deer were observed in the wet 
prairies more and the willow/dense sawgrass less than expected. 
Seasonal shifts also for home range size and distance between 
consecutive locations increased relative to the previous 
experiment, but there was little shift in seasonal habitat-use 
patterns. 

Changes in ^ relative to rut were returned to the levels from the 
previous experiments (decrease of 1 .0 during rut and decrease of 
0.5 just before and after run). 

Weights to calculate the probability of moving to pixely (/" = 1, 2, 
3,. ..,9): 

^j = 0.25 X ;, ^^^.^, + 0.25 X ;, ^^^^ + 0.25 x p ^„i„^^^„„ 

y pixel memory, 

were adjusted during rut, to reflect decreased use the preferred 
habitats. Several experiments were conducted to develop the 
algorithm changes in the final experiment (Table D.8) that were 
not reported in this appendix. 



202 



Table D.8. Summary of final calibration experiment for males. 

Algorithm changes During rut, weights to calculate the probability of moving to pixel 
y(/= 1,2, 3, . . . ,9) were 

n, = 0.23 X p ^,.^, + 0.12 X p ^^^^ + 0.25 x p ^^^^^^ 
+ 0.40 X p , 

f pixel memory, 

and the rest of the year weights were 

Tij = 0.35 X p ^^.^^ + 0. 15 X p ^^,^^ + 0.25 X p ,„„i„g^„„ 
+ 25 X D , 

~^ r Pixel memory' 



Experiment design 2^ fractional factorial with 4 replications of each factor 
combination. Simulations were run for 10 years. 
Fixed parameters were ^=500, X=5, Ar=0.5, MLh=24, MLp=6, 
STEP=250, a=10, P=30, y=60, A^pR=10, Atre=100, Acyp=7.5, 
Aman=10, LDweight=0.4, LDpROB=1.0, MLr=0.5. 

Factor Low High 



Analysis results 



4) 



»^HPR 



^WSA 



2.5 
25 
100 



3 

35 
150 



Based on experimental bum-in time, year 5 data were analyzed. 
Discrepancies for home range size distance, between consecutive 
home range centers, mean distance between locations, and MD 
were minimized with larger (j). Discrepancies for habitat use were 
minimized with larger Ahpr. Awsa=150 produced habitat-use 
patterns closer to those expected than Awsa= 1 00 did by 
significantly increasing mean percentage of observations in 
willow/dense sawgrass. 

Seasonal shifts in habitat-use patterns were present, but not as 
large as observed in the field data. 

Final model settings were determined based on results fi-om this 
experiment (see section 4.4). 



APPENDIX E 
VALIDATION DATA SET 



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206 



Table E.2. Annual and hydrologic season home range sizes for white-tailed deer included 
in the validation data set. 



Deer ID 


Aimual home 


range (ha)° 


Seasonal home range 


(ha)" 


1993 


1994 


93DRY 


94WET 


94DRY 


Female 












89014R 


171 


383 


149 


126 


276 


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450 


- 


274 


988 


- ■ 


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769 


- 


852 


244 


m 


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457 


- 


421 


2138' 


- 


93205 


243 


- 


264 


212 


- 


93206 


123 . 


■ ■: 


118 


100 


- 


93208 


128 


191 


64 


163 


116 


93210 


242 


- 


237 


338 


. 


93211 


381 


- 


293 


196 


- 


93212 


1903"= 


428 


1518' 


2420' 


127 


93214 


456 


- 


285 


801 


- 


93216 


262 


480 


245 


387 


281 


93218 


145 


174 


167 


151 


146 


93219 


126 


85 


99 


103 


50 


93220 


188 


- 


185 


225 


* 


93225 


347 


- 


477 


230 


. 


93227 


173 


509 


132 


314 


338 


93229 


165 


- 


161 


153 


. 


93235 


269 


- 


198 


654 


. 


93237 


238 


- 


416 


198 


72 


94246 


- 


316 


- 


- 


190 


94251 


- 


270 


- 


- 


110 


94261 


- 


325 


- 


. 


232 


Male 












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476 


- 


281 


1218' 


« 


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251 


- 


156 


210 


■„■ 


93204 


214 


- 


107 


- 


a 


93207 


261 


194 


121 


266 , 


n 


93221 


306 


- 


212 


204 


. 


93226 


203 


424 


238 


167 


278 


93233 


135 


- 


109 


111 


_ 


93234 


275 


- 


196 


388 


- 



207 



Table E.2. 


- continued. 




Deer ID 


Annual home range (ha) 


Seasonal home range (ha) 


1993 1994 


93DRY 94WET 94DRY 



Male 



93236 
94244 
94247 
94250 
94252 



115 



76 



175 



290 
347 
349 

211 



207 
129 
176 
97 



" Annual cycles were 1993 (01 Sep 93-31 Aug 94) and 1994 (01 Sep 94-31 Aug 95). 
'' Hydrologic seasons were 93DRY (01 Nov 93 - 30 Apr 94), 94WET (01 May 94 - 3 1 Oct 
94), and 94DRY (01 Nov 94 - 30 Apr 95). 
' Influential outlier, deleted from summary statistics and analyses. 



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LITERATURE CITED 



Agresti, A. 1990. Categorical data analysis. John Wiley & Sons, Inc., New York, New 
York. 

Aitchison, J., and Dunsmore, I. R. 1975. Statistical prediction analysis. Cambridge 
University Press, Cambridge, United Kingdom. 

Akaike, H. 1974. A new look at the statistical model identification. IEEE Transaction on 
Automatic Control AC-19:716-723. 

Alexander, T. R., and A. G. Crook. 1984. Recent vegetational changes in south Florida. 
Pages 199-210 in P. J. Gleason, editor. Environments of south Florida: present 
and past II. Miami Geological Society, Coral Gables, Florida. 

Barrett, M. W., J. W. Nolan, and L. D. Roy. 1982. Evaluation of a hand-held net-gun to 
capture large mammals. Wildlife Society Bulletin 10: 108-1 14. 

Bart, J. 1995. Acceptance criteria for using individual-based models to make management 
decisions. Ecological Applications 5:411-420. 

Beier, P. 1987. Sex differences in quality of white-tailed deer diets. Journal of 
Mammalogy 68:323-329. 

Birch, M. W. 1965. The detection of partial association I: the general case. Journal of the 
Royal Statistical Society B 27: 1 1 1-124. 

Bj0mstad, J. F. 1990. Predictive likelihood: a review. Statistical Science 5:242-254. 

Blake, N. M. 1980. Land into water- water into land: a history of water management in 
Florida. University Presses of Florida, Tallahassee, Florida. 

Boulay, M. C. 1992. Mortality and recruitment of white-tailed deer fawns in the wet 
prairie/tree island habitat of the Everglades. M.S. thesis. University of Florida, 
Gainesville. 

Bovet, P., and S. Benhamou. 1988. Spatial analysis of animals' movements using a 
correlated random walk model. Journal of Theoretical Biology 131:419-433. 



212 



213 

Bowyer, R. T. 1984. Sexual segregation in southern mule deer. Journal of Mammalogy 
65:410-417. 

Box, G. E. P. 1982. Choice of response surface design and alphabetic optimality. Utilitas 
Mathematica 21:11-55. 

Brandt, L. A. 1997. Spatial and temporal patterns of tree islands in the Arthur R. Marshall 
Loxahatchee National Wildlife Refuge. Ph.D. dissertation. University of Florida, 
Gainesville. 

Byford, J. L. 1969. Movement response of white-tailed deer in response to changing food 
supplies. Proceedings of the Southeastern Association of Game and Fish 
Commissioners 23:63-78. 

Clutton-Brock, T. H., F. D. Guiness, and S. D. Albon. 1982. Red deer: behavior and 
ecology of the two sexes. University of Chicago Press, Chicago, Illinois. 

Cochran, W. G., and G. M. Cox. 1957. Experimental designs. Second edition. John Wiley 
& Sons, Inc., New York, New York. 

Conroy, M. J., Y. Cohen, F. C. James, Y. G. Matsinos, and B. A. Maurer. 1995. 

Parameter estimation, reliability, and model improvement for spatially explicit 
models of animal populations. Ecological Applications 5:17-19. 

Craighead, F. C, Sr. 1984. Hammocks of south Florida. Pages 191-198 /n P. J. Gleason, 
editor. Environments of south Florida: present and past II. Miami Geological 
Society, Coral Gables, Florida. 

Cramer, P. A. 1999. Modeling Florida panther movements to predict conservation 

strategies in north Florida. Ph.D. dissertation. University of Florida, Gainesville. 

Davis, S. M., L. H. Gunderson, W. A. Park, J. R. Richardson, and J. E. Mattson. 1994. 
Landscape dimension, composition, and function in a changing Everglades 
ecosystem. Pages 419-444 in S. M. Davis and J. C. Odgen, editors. Everglades: 
the ecosystem and its restoration. St. Lucie Press, Delray Beach, Florida. 

Davis, S. M., and J. C. Odgen. 1994. Introduction. Pages 3-8 in S. M. Davis, and J. C. 
Odgen, editors. Everglades: the ecosystem and its restoration. St. Lucie Press, 
Delray Beach, Florida. 

DeAngehs, D. L., and L. J. Gross, editors. 1992. Individual-based models and approaches 
in ecology: populations, communities, and ecosystems. Chapman «&; Hall, New 
York, New York. 



214 

DeAngelis, D.L., L. J. Gross, M. A. Huston, W. F. Wolff, D. M. Fleming, E. J. Comisky, 
and S. M. Sylvester. 1998. Landscape modeling for Everglades ecosystem 
restoration. Ecosystems 1:64-75. 

Diggle, P. J., K.-Y. Liang, and S. L. Zeger. 1994. Analysis of longitudinal data. Oxford 
Science Publications, Clarendon Press, Oxford, United Kingdom. 

Douglas, M. S. 1947. The Everglades: river of grass. Revised edition, 1988. Pineapple 
Press, Sarasota, Florida. 

Drew, R. D., and N. S. Schomer. 1984. An ecological characterization of the 

Caloosahatchee River/Big Cypress Watershed. FWS/OBS-82/58.2. U.S. Fish and 
Wildlife Service, Metaire, Louisiana. 

Drolet, C. A. 1976. Distribution and movements of white-tailed deer in southern New 

Brunswick in relation to envirormiental factors. Canadian Field Naturalist 90:123- 
136. 

Duever, M. J. 1984. Environmental factors controlling plant conmiunities of the Big 

Cypress Swamp. Pages 127-137 in P. J. Gleason, editor. Environments of south 
Florida: present and past II. Miami Geological Society, Coral Gables, Florida. 

Duever, M. J., J. E. Carlson, J. F. Meeder, L. C. Duever, L. H. Gunderson, L. A. Riopelle, 
T. R. Alexander, R. L. Myers, and D. P. Spangler. 1986. The Big Cypress 
National Preserve. Research Report Number 8, National Audubon Society, New 
York, New York. 

Duever, M. J., J. F. Meeder, and L. C. Duever. 1984. Ecosystems of the Big Cypress 

Swamp. Pages 294-303 in K. C. Ewel and H. T. Odum, editors. Cypress swamps. 
University Presses of Florida, Gainesville, Florida. 

Dunning, J. B., Jr., D. J. Stewart, B.J. Danielson, B. R. Noon, T. L. Root, R. H. 

Lamberson, and E. E. Stevens. 1995. Spatially explicit population models: current 
forms and future uses. Ecological Applications 5:3- 11. 

Fermema, R. J., C. L. Neidrauer, R. A. Johnson, T. K. Mac Vicar, and W. A. Perkins. 
1994. A computer model to simulate natural Everglades hydrology. Pages 249- 
290 in S. M. Davis and J. C. Odgen, editors. Everglades: the ecosystem and its 
restoration. St. Lucie Press, Delray Beach, Florida. 

Fleming, D.M., D.L. DeAngelis, L.J. Gross, R.E. Ulanowicz, W.F. Wolff, W.F. Loftus, 
and M.A. Huston. 1994. ATLSS: Across-trophic-level system simulation for the 
Everglades and Big Cypress Swamp. National Biological Service Technical 
Report, Miami, Florida. 



215 

Flohrschutz, E. W. 1978. Dwarf cypress in the Big Cypress Swamp of southwestern 
Florida. M.S. thesis. University of Florida, Gainesville. 

Gavin, T. A., L. H. Suring, P. A. Vohs, Jr., and E. C. Meslow. 1984. Population 

characteristics, spatial organization, and natural mortality in the Columbian white- 
tailed deer. Wildlife Monographs 91. 

Gelman, A., J. B. Carlin, H. S. Stem, and D. B. Rubin. 1995. Bayesian data analysis. 
Chapman & Hall, London, United Kingdom. 

Gentry, R. C. 1984. Hurricanes in south Florida. Pages 510-519 in P. J. Gleason, editor. 
Environments of south Florida: present and past II. Miami Geological Society, 
Coral Gables, Florida. 

Grimm, V. 1999. Ten years of individual-based modelling in ecology: what have we 
learned and what could we learn in the future? Ecological Modelling 1 15: 129- 
148. 

Gunderson, L. H. 1990. Historical hydropattems in wetland communities of Everglades 
National Park. Pages 1099-1 1 1 1 /« R. R. Sharitz and J. W. Gibbons, editors. 
Freshwater wetlands and Wildlife. CONF-8603101, DOE Symposium Series No. 
61. USDOE Office of Scientific and Technical Information, Oak Ridge, 
Tennessee. 

Gimderson, L. H. 1994. Vegetation of the Everglades: determinants of community 

composition. Pages 323-340 in S. M. Davis and J. C. Odgen, editors. Everglades: 
the ecosystem and its restoration. St. Lucie Press, Delray Beach, Florida. 

Gunderson, L., and L. L. Loope. 1982a. A survey and inventory of the plant communities 
in the Pinecrest area. Big Cypress National Preserve. National Park Service, South 
Florida Research Center Report T-655. Everglades National Park, Homestead, 
Florida. 

Gunderson, L., and L. L. Loope. 1982b. An inventory of the plant communities within the 
Deep Lake Strand area. Big Cypress National Preserve. National Park Service, 
South Florida Research Center Report T-666. Everglades National Park, 
Homestead, Florida. 

Gunderson, L., L. L. Loope, and W. R. Maynard. 1982. An inventory of the plant 

communities in the Turner River area. Big Cypress National Preserve, Florida. 
National Park Service, South Florida Research Center Report T-648. Everglades 
National Park, Homestead, Florida. 

Hanski, I. A., and M. E. Gilpin. 1996. Metapopulation biology: ecology, genetics, and 
evolution. Academic Press, San Diego, California. 



216 



Holgate, P. 1971. Random walk models for animal behavior. Pages 1-12 /« G. Patil, E. 
Pielou, and W. Walters, editors. Statistical ecology: sampling and modeling of 
biological populations and population dynamics. Pennsylvania State Statistics, 
Volume 2. Pennsylvania State University Press, University Park, Pennsylvania. 

Hunter, C. 1990. Odocoileus virginianus seminolus: the ecology of fawning in wet and 
dry prairies. M.S. thesis, University of Florida, Gainesville. 

Hurd, C. C, R. F. Labisky, and J. R. Snyder. 1995. Food habits of fawn and adult white- 
tailed deer in the wet prairie of the Everglades. Department of Wildlife Ecology 
and Conservation, University of Florida, Gainesville. (Typescript.) 

Huston, M., D. DeAngelis, and W. Post. 1988. New computer models unify ecological 
theory. BioScience 38:682-691. 

1ms, R. A. 1995. Movement patterns relates to spatial structures. Pages 85-109 in L. 

Hansson, L. Fahrig, and G. Merriam, editors. Mosaic landscapes and ecological 
processes. Chapman & Hall, London, United Kingdom. 

Khuri, A. I., and J. A. Cornell. 1987. Response surfaces: designs and analyses. Marcel 
Dekker, Inc., New York, New York. 

Kleijnen, J. P. 1987. Statistical tools for simulation practitioners. Marcel Dekker, Inc., 
New York, New York. 

Kushlan, J. A. 1990. Freshwater marshes. Pages 324-363 in R. L. Myers and J. J. Ewel, 
editors. Ecosystems of Florida. University of Central Florida Press, Orlando, 
Florida. 

Labisky, R. F., M. C. Boulay, R. A. Sargent, K. E. Miller, and J. M. Zultowsky. 1995. 
Population dynamics of white-tailed deer in the Big Cypress National Preserve 
and Everglades National Park. Final Report to USDI-National Park Service. 
Department of Wildlife Ecology and Conservation, University of Florida, 
Gainesville. 

Labisky, R. F., K. MacDonald, C. S. Hartless. 1997. Behavioral responses of white-tailed 
deer along the spatial transition between hunted and nonhunted populations. Final 
Report to USDI-National Park Service. Department of Wildlife Ecology and 
Conservation, University of Florida, Gainesville. 

Labisky, R. F., K. E. Miller, and C. S. Hartless. 1999. Effect of Hurricane Andrew on 
survival and movements of white-tailed deer in the Everglades. Journal of 
Wildlife Management 63:872-879. 

Lampton, B. 1982. Controversy in the 'Glades. Florida Wildlife 36:12-18. 



217 

Langenau, E. E., Jr., S. R. Kellert, and J. E. Applegate. 1984. Values in management. 

Pages 699-720 in L. K. Halls, editor. White-tailed deer: ecology and management. 
Stackpole Books, Harrisburg, Peimsylvania. 

Lefkovitch, L. P. 1965. The study of population growth in organisms grouped by stages. 
Biometrics 21:1-18. 

Leslie, P. H. 1945. On the use of matrices in certain population mathematics. Biometrika 
33:183-212. 

Levins, R. 1969. Some demographic and genetic consequences of enviroimiental 

heterogeneity for biological control. Bulletin of the Entomological Society of 
America 15:237-240. 

Lewis, M. A., and J. D. Murray. 1993. Modelling territoriality and wolf-deer interactions. 
Nature 366:728-740. 

Light, S. S., and J. W. Dineen. 1994. Water control in the Everglades: a historical 

perspective. Pages 47-84 in S. M. Davis and J. C. Odgen, editors. Everglades: the 
ecosystem and its restoration. St. Lucie Press, Delray Beach, Florida. 

Littell, R. C, G. A. Milliken, W. W. Stroup, and R. D. Wolfmger. 1996. SAS® System 
for mixed models. SAS Institute Inc., Gary, North Garolina. 

Liu, J. 1993. EGOLEGON: and EGOLogical-EGONomic model for species conservation 
in complex forest landscapes. Ecological Modelling 70:63-87. 

Liu, J., J. B. Dunning, Jr., and H. P. Pulliam. 1995. Potential effects of a forest 

management plan on Bachman's sparrows {Aimophila aestivalis): linking a 
spatially explicit model with GIS. Gonservation Biology 9:62-75. 

Loveless, G. M. 1959a. A study of the vegetation of the Florida Everglades. Ecology 
40:1-9. 

Loveless, G. M. 1959b. The Everglades deer herd: life history and management. 
Technical Bulletin 6, Florida Game and Fresh Water Fish Gommission, 
Tallahassee, Florida. 

MacDonald, K. 1997. Site fidelity and its effects on survival of Odocoileus virginianus 

seminolus during a catastrophic flood in the Everglades. M.S. thesis. University of 
Florida, Gainesville. 

Maehr, D. S., R. G. Belden, E. D. Land, and L.Wilkins. 1990. Food habits of panthers in 
southwest Florida. Journal of Wildlife Management 54:420-423. 



*;,, 



218 

Maehr, D. S., and J. R. Brady. 1986. Food habits of bobcats in Florida. Journal of 
Mammalogy 67 : 1 3 3 - 1 3 8 . 

Main, M. B., and B. E. Coblentz. 1990. Sexual segregation among ungulates: a critique. 
Wildlife Society Bulletin 18:204-210. 

Main, M. B., F. W. Weckerly, and V. C. Bleich. 1996. Sexual segregation in ungulates: 
new directions for research. Journal of Mammalogy 77:449-461. 

Manly, B.F. J., L. I. McDonald, and D. L. Thomas. 1993. Resource selection by animals: 
statistical design and analysis for field studies. Chapman and Hall, London, 
United Kingdom. 

Marchington, R. L., and D. H. Hirth. 1984. Behavior. Pages 129-168 in L. K. Halls, 

editor. White-tailed deer: ecology and management. Stackpole Books, Harrisburg, 
Pennsylvania. 

Mayer, D. G., and D. G. Butler. 1993. Statistical validation. Ecological Modelling 6821- 
32. 

McCullough, D. R. 1979. The George Reserve deer herd: population ecology of a K- 
selected species. University of Michigan Press, Ann Arbor, Michigan. 

Michael, E. D. 1970. Activity patterns of white-tailed deer in south Texas. Texas Journal 
of Science 21:417-428. 

Miller, K. E. 1993. Habitat use by white-tailed deer in the Everglades: tree islands in a 
seasonally flooded landscape. M.S. thesis, University of Florida, Gainesville. 

Miquelle, D. G., J. M. Peek, and V. Van Ballenberghe. 1992. Sexual segregation in 
Alaskan moose. Wildlife Monographs 122. 

Montgomery, D. C. 1991. Design and analysis of experiments. Third edition. John Wiley 
& Sons, Inc., New York, New York. 

Montgomery, G. G. 1974. Communication in red fox dyads: a computer simulation study. 
Smithsonian Contributions to Zoology, Number 187. Smithsonian Institution 
Press, Washington, D.C. 

Murdoch, W. W., E. McCauley, R. M. Nisbet, S. C. Gumey, and A. M. de Roos. 1992. 

Individual-based models: combining testability and generality. Pages 18-35 in D. 
, ^ , L. DeAngelis and L. J. Gross, editors. Individual-based models and approaches in 

ecology: populations, communities, and ecosystems. Chapman & Hall, New York, 

New York. 



219 

Nelson, M. E., and L. D. Mech. 1984. Home range formation and dispersal of deer in 
northeastern Minnesota. Journal of Mammalogy 65:567-575. 

Neu, C. W., C. R. Byers, and J. M. Peek. 1974. A technique for analysis of utilization- 
availability data. Journal of Wildlife Management 38:541-545. 

Nisbet, R. M., and Gumey, W. S. C. 1982. Modelling fluctuating populations. John Wiley 
& Sons, Inc., New York, New York. 

Odgen, J. C. 1994. A comparison of wading bird nesting colony dynamics (1931-1946 
and 1974-1989) as an indication of ecosystem conditions in the southern 
Everglades. Pages 533-570 in S. M. Davis and J. C. Odgen, editors. Everglades: 
the ecosystem and its restoration. St. Lucie Press, Delray Beach, Florida. 

Olmsted, I. C, and T. V. Armentano. 1997. Vegetation of Shark Slough, Everglades 
National Park. National Park Service, South Florida Natural Resources Center 
Report 97-001. Everglades National Park, Homestead, Florida. 

Olmsted, 1. C, L. L. Loope, and R. E. Rintz. 1980. A survey and baseline analysis of 
aspects of the vegetation of Taylor Slough, Everglades National Park. National 
Park Service, South Florida Research Center Report T-586. Everglades National 
Park, Homestead, Florida. 

Pearl, R., and L. J. Reed. 1920. On the rate of growth of the population of the United 

States since 1790 and its mathematical representation. Proceedings of the National 
Academy of Science USA 6:275-288. 

Power, M. 1993. The predictive validation of ecological and environmental models. 
Ecological Modelling 68:33-50. 

Pulliam, R. H., J. B. Dunning, Jr., and J. Liu. 1992. Population dynamics in complex 
landscapes: a case study. Ecological Applications 2:165-177. 

Rao, C. R. 1977. Prediction of future observations with special reference to linear models. 
Pages 193-208 in P. R. Krishnaiah, editor. Multivariate analysis IV: proceedings 
of the fourth international symposium on multivariate analysis. North-Holland 
Publishing Company, Amsterdam, Netherlands. 

Renshaw, E. 1990. Modelling biological populations in space and time. Cambridge 
University Press, Cambridge, United Kingdom. 

Richter, A. R., and R. F. Labisky. 1985. Reproductive dynamics among disjunct white- 
tailed deer herds in Florida. Journal of Wildlife Management 49:964-97 1 . 



220 

Risenhoover, K. L., H. B. Underwood, W. Yan, and J. L. Cooke. 1997. A spatially 

explicit modeling environment for evaluating deer management strategies. Pages 
366-379 in W. J. McSchea, H. B. Underwood, and J. H. Rappole, editors. The 
science of overabundance: deer ecology and population management. Smithsonian 
Institution Press, Washington, D.C. 

Rolfe, F. J., and D. Davenport. 1969. Simulation of simple models of animal behavior 
with a digital computer. Journal of Theoretical Biology 23:400-424. 

Rykiel, E. J., Jr. 1996. Testing ecological models: the meaning of validation. Ecological 
Modelling 90:229-244. 

Saarenmaa, H., N. D. Stone, L. J. Folse, J. M. Packared, W. E. Grant, M. E. Makela, and 
R.N. Coulson. 1988. An artificial intelligence modelling approach to simulating 
animal/habitat interactions. Ecological Modelling 44:125-141. 

Sanderson, G. C. 1966. The study of mammal movements - a review. Journal of Wildlife 
Management 30:215-235. 

Sargent, R. A., Jr. 1992. Movement ecology of adult male white-tailed deer in hunted and 
non-hunted populations in the wet prairie of the Everglades. M.S. thesis, 
University of Florida, Gainesville. 

Sargent, R. A., and R. F. Labisky. 1995. Home range of male white-tailed deer in hunted 
and non-hunted populations. Proceedings of the Aimual Conference of the 
Southeastern Association of Fish and Wildlife Agencies 49:389-398. 

Sargent, R. E. 1984. A tutorial on verification and validation of simulation models. Pages 
1 15-122 in S. Sheppard, U. Pooch, and D. Pegden, editors. Proceedings of the 
1984 Winter Simulation Conference. IEEE 84CH2098-2. 

Scholl, D. W. 1968. Mangrove swamps. Pp. 684-688 in R. W. Fairbridge, editor. 

Encyclopedia of geomorphology. Reinhold Publishing Corporation, New York, 
New York. 

Schomer, N. S., and R. D. Drew. 1982. An ecological characterization of the lower 

Everglades, Florida Bay, and the Florida Keys. FWS/OBS-82/58. 1 . U.S. Fish and 
Wildlife Service, Office of Biological Services, Washington, D.C. 

Seaman, D. E., and R. A. Powell. 1996. An evaluation of the accuracy of kernel density 
estimators for home range analysis. Ecology 77:2075-2085. 

Shank, C. C. 1982. Age-sex differences in the dies of wintering Rocky Mountain bighorn 
sheep. Ecology 63:627-633. 



7U 

Silverman, B. W. 1986. Density estimation for statistics and data analysis. Chapman and 
Hall, London, United Kingdom. 

Siniff, D. B., and C. Jessen. 1969. A simulation model of animal movement patterns. 

Pages 185-219 in J. B. Cragg, editor. Advances in ecological research. Volume 6. 
Academic Press, London, United Kingdom. 

Skellam, J. G. 1951. Random dispersal in theoretical populations. Biometrika 38- 196- 
218. 

Sparrowe, R. D., and P. F. Springer. 1970. Seasonal activity patterns of white-tailed deer 
in eastern South Dakota. Journal of Wildlife Management 34:421-431. 

Thomas, D. L., and E. J. Taylor. 1990. Study designs and tests for comparing resource use 
and availability. Journal of Wildlife Management 54:322-330. 

Turner, M. G., Y. Wu, W. H. Romme, and L. L. Wallace. 1 994. Simulating winter 

interactions among ungulates, vegetation, and fire in northern Yellowstone Park. 
Ecological Applications 4:472-496. 

Turner, M. G. G. L. Arthaud, R. T. Engstrom, S. J. Heil, J. Liu, S. Loeb, and K. 

McKelvey. 1995. Usefulness of spatially explicit population models in land 
management. Ecological Applications 5:12-16. 

U.S. Geological Survey, Biological Resources Division. 1997. ATLSS: across-trophic- 
level system simulation: an approach to analysis of south Florida ecosystems. 
USGS Technical Report. Miami, Florida. 

Van der Molen, D. T., and J. Pinter. 1 993. Environmental model calibration under 

different specifications: an application to the model SED. Ecological Modelline 
68:1-19. ^ 

Vemer, J., K. S. McKelvey, B. R. Noon, R. J. Gutierrez, G. I Gould, Jr., and T. W. Beck, 
(technical coordinators). 1992. The California spotted owl: a technical assessment 
of its current status. Gen. Tech. Rep. PSW-GTR-133. Pacific Southwest Research 
Station, Forest Service, U.S. Department of Agriculture, Albany, California. 

Vonesh, E. F., and V. M. Chinchilli. 1997. Linear and nonlinear models for the analysis '^ 
of repeated measurements. Marcel Dekker, Inc., New York, New York. 

White, G. C, and R. A. Garrott. 1990. Analysis of wildlife radio-tracking data. Academic 
Press, Inc., San Diego, California. 

Worton, B. J. 1989. Kernel methods for estimating the utilization distribution in home- 
range studies. Ecology 70:164-168. 



222 



Zultowsky, J. M. 1992. Behavioral and spatial ecology of female white-tailed deer in the 
Everglades ecosystem. M.S. thesis. University of Florida, Gainesville. 



BIOGRAPHICAL SKETCH 

Christine Steible Hartless was bom on 8 September 1968 in South Bend, hidiana. 
She received a B.S. in animal science-equine option with a minor in agricultural 
economics from the University of Kentucky in 1 990. While at the University of 
Kentucky, she worked for the swine nutrition group of the Department of Animal Science 
in the field, in the lab, and in front of a computer. It was here, doing elementary data 
analyses, that her interest in statistics was bom. She entered the graduate program in the 
Department of Statistics at the University of Florida in August 1991 and was graduated 
with a Master of Statistics in May 1993. While working on her master's degree and 
taking course work towards a Ph.D. in statistics, she worked as a graduate consultant in 
the statistical consulting lab for the histitute of Food and Agricultural Sciences (IFAS) at 
the University of Florida. This consulting experience led her to seek a field where she 
could apply her statistics knowledge to environmental issues. In January 1996, she 
changed doctoral programs and entered the graduate program in the Department of 
Wildlife Ecology and Conservation, and she was graduated with a Ph.D. in August 2000. 



223 



I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fiilly adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. 



-^ixXt/X ^' ■ O^^Cu<iAc/ 



Ronald F. Labisky, Chairman ./ 
Professor of Wildlife Ecology and 
Conservation 



I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. -— - — 



/l€i-tiy/A^ ni -^^ 




Kenneth M. Portier, Cochairman 
Associate Professor of Statistics 



I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and qualify, 
as a dissertation for the degree of Doctor of Philosophy. 




'U-Sc^ H/-r^/fj^^ 



'•^ George W. Tanner 

Professor of Wildlife Ecology and 



Conservation 

I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. 



C/lClichael P. Moulton < . 




■Ja^ 



Associate Professor of Wildlife Ecology and 
Conservation 



I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. 

^ Jon C. Allen 

\ Professor of Entomology and Nemotology 






J 



•ft ,.Jt.'-^.,,.Ji 



n 
'w 



This dissertation was submitted to the Graduate Faculty of the College of 
Agricultural and Life Sciences and to the Graduate School and was accepted as partial 
fulfillment of the requirements for the degree of Doctor of Philosophy. 

August 2000 






Dean, College of Agricultural ^ndDjfe^^ 
Sciences 




Dean, Graduate School 




.v\?x3\ 



UNIVERSITY OF FLORIDA 



3 1262 08555 1835